I understand that the process of colonizations varied wildly by regions, powers and centuries, but I have the feeling that there are some clear differences between how different powers did colonialism. I think it is easy to appreciate at least 3 different approaches.
For the first approach I'm thinking for example of Dutch colonialism in the Dutch East Indies. In Indonesia they seem to have left very little cultural impact. There is very few architectural and infrastructure remains from the time. The Bahasa Indonesia has just some loan words of dutch origin here and there, and the people seem to be fenotipically south east asian. That seems like colonialism with very little cultural impact and without any visible attempts at making life better for the colonies. Seems like purely economical exploitation.
For the second I can think of most spanish colonies in the americas. The spanish have left a clear cultural impact including cuisine, language, religion and traditions. On top of that there was a clear attempt at changing those regions to make them more spanish-like. Some examples can be constructing large expensive cathedrals, or universities even on the first few decades of the conquest. And the spanish population mixed together with the native population, so fenotipically people look often mixed. Looks more like an attempt to incorporate the population and the land to the conquering nation.
Finally for the third approach, I would consider some sort of "substitution" colonialism, such as USA, Canada, Argentina or Australia, where the population has mostly non-native ancestry and the cities are very european, with the native population mostly confined to reservations. Looks like an attempt at incorporating the land, excluding the native people, to the conquering nation.
It seems to me that in the case of british, french and dutch colonialism it could be related to the weather. In places with more european-like weather (North America, South Africa, Oceania) they went for the 3rd approach while in most of Africa, India or Asia they seem to have used the 1st. In any case avoiding to mix with the local population. But the case of spanish colonies seems less clear to me. I would say they used the 1st approach in the Philipines and Africa, the 2nd in most of South and Central America (including jungle regions) and the 3rd in Argentina and Chile. Is there any kind of pattern? Where the spanish simply more willing to mix with the locals? How does the approach of other colonial powers like Portugal or Germany compare? Am I oversimplifying way too much?
I think making a simple thesis of "this country colonizes in this manner because of these climatic facts" is oversimplifying it. The outcome and strategies of colonization varied wildly depending on local circumstances, climate, culture, politics and resources, as well as the specific circumstances of the colonizer at the specific time.
However with that said, over time the different colonizing powers did unconsciously develop different strategies, formed by their different cultural baggage and different strategies, and you can draw some overarching themes from it.
If we start with the first colonial power, Portugal, when colonizing Asia, they quickly adapted to local circumstances. That is, they learned they were dealing with powerful local Asian rulers, and their only significant advantage was naval power. For this reason, the Portuguese developed the strategy of capturing key naval cities to establish naval supremacy, but largely avoiding large scale territorial acquisitions. In this manner htey managed to effectively control sea lanes in Asia for much of a century with minimal manpower investments, and no real settler colonies - only a minority of Portuguese emigrants were women for instance. This strategy also applied to Africa, and over time, Brazil was the only true Portuguese settler colony, mostly because the value in Brazil, sugar, had to be produced by the Portuguese "themselves" - by this I mean slavery of Africans.
It is notable that while the Portuguese Empire enriched the Portuguese colonials, it did little to transform the world of trade they engaged with. Portugal never truly developed great power ambitions with their empire.
This is probably one of the key reasons for the difference with the second European colonial power, Spain. From the beginning, the Spanish Empire was entwined with Spains great power ambitions in Europe, and was largely the engine of said ambitions. Therefore, the reach of the Spanish Empire was much wider than the Portuguese. Of course, this ambition was also fed by initial Spanish success in America. Having quickly conquered the vast Aztec and Inca Empires seemingly with little effort, Spanish colonialism was characterised by the ambition of military contorl over vast areas of territory, and also the belief in Spanish right to politically dominate non-European territories. The spread of Catholicism was also a much more central political goal for Spain than for Portugal, once again tied to Spanish power in Europe - the Spanish king regarded himself as the defender of Catholicism against Islam, Protestantism and Heathen faiths. Therefore, the conversion of colonials to Catholicism was a political goal in and of itself, that directly motivated decisions. This was not the case for Portugal to nearly the same extent.
This difference becomes extra apparent in the case of Spanish colonialism in Asia. The Spanish colonies in Asia, starting with the Philippines, were essentially offshoots of their American colonies, and the Spanish strategy in Asia was originally to mimic that in America - spread Catholicism and conquer vast territories. This led to the conception of comically unrealistic plans like Spanish plans to conquer both Japan and China with a few hundred men. Arguably, this misunderstanding of Asian circumstances also severely limited Spanish expansion in Asia. Ultiamtely all their many ventures outside the Philippines ended up being short-lived failures, including military expeditions to Siam, Cambodia, Borneo, Ternate and Taiwan. This was also often to the frustration of Spanish merchants, who wanted to profit off trade, but whose interests were often brushed aside in favor of geopolitical and religious goals.
The thrid colonial power, who arguably left the blueprint for later ones, were the Dutch. They were significant in being the first to be driven by private companies, the West and East India Companies, singularly devoted to profit. Missionary activity played a very minor role in Dutch colonialism, and there was no coherent strategic planning - territory was acquired at the expectation of being profitable, and readily abandoned if it wasn't immediately profitable. In this way, I think you are not wrong to say the Dutch colonialism was the closest you get to colonialism that was purely for economic exploitation. In this manner it was arguably more similar to the Portuguese than the Spanish. Unlike the Portuguese however, Dutch colonialism was also closely tied to Dutch ambitions in Europe - in fact, the Netherlands originally became a colonial power as part of their war of independence against Spain, the colonial ventures of the Dutch were intended to cripple the Spanish economy and thereby gain advantages in Europe. The Dutch colonial empire was also an essential backbone of Dutch economic power in Europe.
With that said however, the Dutch did also establish certain settler colonies, reminiscent of your 3rd kind of colonialism. The Dutch New Netherlands colony in North America, the slave colonies of the West Indies and Brazil, and probably the one place they had their most lasting cultural impact, in South Africa. So once again, you cannot make these neat groupings of nations.
British colonialism was - as many other contemporary smaller nations, like Denmark, Sweden and the German states - based on the successful Dutch model. Missionary activity took a secondary role, and the main goals were largely economical. Many English colonies were however established by religious minorities, something that didn't happen in the Netherlands, having freedom of religion. I'd argue that in the early time period, English/British colonialism followed a similar pattern to the Dutch. It was also in many regards a product English rivalry wit the Netherlands in the 17th century. Later, British colonialism became more imperial in nature, but the British Civilizing Mission with schools, hospitals, and large scale infrastructure projects did not occur until the high age of imperialism in the 19th century.
The last of the traditional major colonial powers was France, a bit late ot the party as they only really started in the late 17th century after a few starts in North America. Under Louis XIVth, colonialism was also closely tied to the spread of French power and influence, and especially to the status of France as a leading European power. The status thing was quite important for most colonial projects, having far away colonies was simply prestiguous by this time. For France, apart from in North America, where colonialism was more directed through immediate economic goals and there were few larger ambitions, colonialism had clear political goals. Promoting French influence at the course of especially British and Spanish. The use of French Catholic missionaries to compete with those controlled by Rome was also essential in this process.
The final model I want to emphasize, because I think its too often ignored, is Russia. Russian conquest of Siberia was way less coordinated and controlled than other colonial powers, and sometimes it isn't even fully considered colonialism, but I think it deserves mention. It was largely driven by individuals with immediate economic concerns, and had no overarching strategic goals - Moscow was unwilling to commit resources to it, and htey didn't compete with other colonial powers and thereby gain advantages in Europe in any meaningful sense. Russian colonialism was brutal, and missionary activity was almost nonexistent until the reign of Catherine the Great. There was also no coherent plans of territorial gain, if territories proved unprofitable and difficult to hold, they were readily abandoned, as happened with the Amur region. I think Russian colonialism holds a unique spot in the overall story.
In all I would say what approach to colonialism a colonial venture has has more to do with time and place than colonial power. The Netherlands and Britain made settler colonies in North America but purely economic colonies in Asia at the same time for instance. However, it is also true that the nature of colonialism is tied to the ambitions of the state in Europe. A state with European great power ambitions will have different goals with colonialism than one who does not. If the state does not see clear political benefits to colonialism, it is likely that it is left largely to individuals, who put profits above long-term strategic goals. This is most clear when comparing Spain and the Netherlands for instance.
This became a very long answer, but in my defence, the question is complicated. I hope it helped shed light on your question, even if ti is hard to fully answer.