What was life like in Western Europe and Britain during the Roman Empire's control at it's height?

I should start by saying that this is a question that is basically unanswerable. People in the Roman Empire lived lives that were just as rich, complex and diverse as people do today. And I think we can all agree that "what is your life like" would be a difficult question for even a single individual to answer, let alone several million. Anyway. That being said, I'll try to give a couple of broad strokes that can help you "fill in" your mental landscape, and I am happy to expand on whatever I can. The date range I am largely looking at will be second century CE.

From the most zoomed out level, the Roman Empire was roughly divided into two halves: the Latin West and the Greek East. This is a distinction the Romans themselves were aware of, but not as much as we are, who are aware of the eventual trajectory towards a formal split of the two halves. The division is linguistic, but this gets a little messy when we think of "everyday" language, so broadly speaking think of this as a distinction in public discourse. People in Syria still spoke Syriac, people in Gaul still spoke Celtic, but when writing literature or making inscriptions they used Latin and Greek. But these linguistic features also map onto more important ones: by and large, the Greek East had a long history of centralized urban states before the Roman conquest, while the Latin West did not. There are massive exceptions to this, the most obvious being North Africa in the West and the upper Balkan regions in the East. Still, this broadly holds true, and perhaps because of this the East was significantly wealthier and more populace than the West. I often hear an estimate that about 70% of the Roman Empire's population and wealth was in the East. certainly, the only "mega-cities" in the Empire were in the East, Italy, and North Africa.
For the cities, urbanization rates varied greatly across provinces. For Italy, you might be looking at something around a 30% urbanized population--an exceptionally high rate for which we have to thank an imperial system that could direct the flow of provincial grain to the center. North Africa will also be very high, perhaps 20% although there really has not been the sort of exploration of rural settlements necessary to describe this. Gaul would be at around (EDIT)10% and Britain will be at perhaps a 5% urbanization rate, the great majority of them living in what are termed "small towns" of around 5000. In Britain, cities don't really get larger than about 20,000 except for London. To help you visualize this, the Roman population of Pompeii was probably about 20,000, but it was significantly more compact than any city in Britain. Where Pompeii was a city with a tightly ordered grid crowded within a city wall, Romano-British cities had open spaces and did not spread out to the wall. Furthermore, where Pompeian houses were atrium-style, basically squares with a courtyard of a type still seen in many Mediterranean contexts today, British buildings are corridors and tabernae--think rectangles open on a narrow end. There are plenty of exceptions, and certainly atria are not rare in Britain, but these are general types.
Incidentally, I will largely be taking Britain and Italy as my contrast, and think of Gaul as a continuum between the two. Southern Gaul looks a lot like Italy, northern Gaul looks a lot like Britain. Gaul was by and large more urbanized than Britain, and had larger cities with more wealth.
So how did people live in cities? What was their work? Again, it depended on where you were. Quite a few of the small towns were what can be termed "agro-towns", that is, they were settlements in which the primary activity was agriculture and a significant portion of the population worked in fields surrounding the city. This certainly required specialized labor--think blacksmiths, bakers, potters, etc--but this was largely in support of agricultural activity rather than the reverse. In very large cities, on the other hand, a true urban economy prevailed, with rents, wage labor, highly specialized crafts, permanent shops, a steady rural influx and more. In between you can find all sorts of different types of urban spaces, one I am familiar with is on the site of the modern Bourton-on-the-Water, which was a mining settlement. In northern Britain, on the other hand, urban spaces would largely exist to support military sites, York being a well known example.
So how about the countryside? The classic roman farming site is the villa. The term "villa" is notoriously complex: to the Romans, it evoked an idea of a luxurious retreat. To archaeologists, it basically just means a rural dwelling large enough that we call it a villa. I have seen a "villa" four rooms in a line about 15-20 meters in total, and I have seen a villa where the gateway is 30 meters across and two or three stories high. So these vary a lot. Their agricultural strategies varied a great deal as well. Some villas largely focused on self subsistence, growing a bit of everything and selling surpluses. Some basically pursued cash crop strategies. Some were centers of pastoralism, some were centers of industry, some had massive fish ponds, and some were basically holiday getaways. I have even seen some centered around religious sites and one in Britain that has a bath so large that it may have served as a spa. One characteristic of the Roman empire is a great diversity of potential economic strategies.
What about those not in villas? Certainly, there are examples of a "manorial" pattern that later characterized Medieval demography, in which a high status dwellings are ringed by a village, but more characteristic is a dispersed pattern of settlement, distinctive to the Roman period, in which most rural settlement was in the form of single dwellings or small hamlets. The farmers here would primarily farm for subsistence, but they were still integrated into the wider economy. For example, the pottery and roof tiles found at "peasant" dwellings are largely not home built, and probably the same went for tools. Our evidence points towards money being the primary medium of exchange, not barter.
A quick note on slaves: people love to insert slaves everywhere to a rather comical degree, and do so without any real care for actual evidence. You will often hear a casual claim that "x was done by slaves" or "slaves would be working in y" without any real reason to think that slaves were actual the dominant working group. Certainly slaves did exist, but where we have evidence (for example, the Vipsaca tablets describing mining operations in Portugal) we see free wage labor being dominant. More strikingly, the evidence for rural slaves is actually pretty poor: they are mentioned in agricultural handbooks so we know they existed, but, for example, slave quarters are notoriously not present archaeologically. This isn't a fairy tale, and stoking the furnaces of a bath is a miserable job no matter whether you are free or enslaved, and free workers there are likely forced to work by circumstance, but if we want to accurately populate a landscape I feel we need to step back from a reflexive identification of slaves everywhere.
For a final note on social structure and religion, by and large we see continuations of patterns developed before the conquests. For example, in Italy people largely group identify themselves by gens, or extended family. In Britain, it tends to be by civitas, the socio-political unit that existed before the Roman conquest and was how the province was divided administratively. Religion also shows a great deal of continuity. For example, in Britain "classical" temples, which tend to be a central structure in the forum of an ideal Roman town, are rare (I don't know of any outside of a major political city), but Gallo-Roman temples are extremely common. What changes religiously is that incorporation to the empire suddenly adds many more ingredients to the religious stew, so alongside a native veneration of Epona, for example, there might be worship of Mithras. Christianity is naturally the premier example of this.

This is a very broad view, and largely focused by necessity on economy and settlement patterns. I can try to flesh out any point you may wish. I'm not aware of a good one-stop shop for Roman life, but I would suggest Kevin Greene's Archaeology and the Roman Economy for economic questions and Greg Woolf's Rome: An Empire's Story for social questions.