This is going to depend widely on the nation, you should specific your question a little more if you want a better answer from some of the really good contributors they have here.
It was quite common for European nations to use purchased officer commissions. Thus as a wealthy young man of gentle birth, you would be expected to pay a set amount of money to the regiment of your choice, and receive a commission. Britain is a prime example.
Additionally, if you were really wealthy and connected, you would be able to get permission to create a regiment during wartimes. Which would automatically make you the Colonel. A regiment was a semi-independent military unit, which would be gathered into armies. They were responsible for all their own equipment and training, and would often be quite eclectic. Some regiments were permanent institutions, most were temporary to a war.
Part of the whole reason of purchasing commissions was to keep people of no stature out of the officer class. So your aristocratic background was absolutely relevant, and would get you great benefits for your military career. If you're not aristocratic but just rich, do not despair! There are also the corporate militaries that hired and promoted based on social position and connections as well. You didn't even need to be a citizen of the appropriate country for those most of the time either, as they were always looking for skilled and motivated (as well as proper) people.
Most of my knowledge of the British system is coming from this book (which is specific to India), which I recommend: Its very interesting and covers both the corporate soldiers of the east India company and the British soldiers themselves. I don't have it with me or I'd be able to give you more detailed information.
Sahib: The British Soldier in India 1750-1914, by Richard Holmes
For Sweden, this is a bit complicated.
You could join Adelsfanan, the noble cavalry regiment, but it became a paper regiment only after mustering for the last time 1743. After that the regiment became a theoretical organisation where noblemen reported their adress to their company commander once per year and were thus spared some other duties and crown fees.
If you wanted to be part of the actual military, you would have a good chance to become an officer in the indelta army. When Sweden entered the Pommeranian War (the Swedish participation in the Seven Years' War) in 1757 the army had 400 non-noble officers to 1 400 of noble extraction.
Before the creation of the Kungliga Krigsakademin (Royal War Academy) at Karlberg 1792, noblemen that were inclined to a military career would often start as privates or NCOs with the knowledge that they were to be promoted to officer as soon as a position was ready. Promotions were often done in chains - when a regimental commander retired, a major was promoted to colonel, a captain to major, a lieutenant to captain and so on, as positions became available. The system was thus based on positions that were at least in theory filled based on merits, but in reality as corruption and lethargy afflicted the Swedish army on the collapse of the Swedish Empire after the defeat in the Great Nordic War, contacts were what you needed to get a position. And noble-men usually had much better contacts.
You could improve your chances of getting an available officer's position by serving abroad in one of the mercenary or rented regiments (nations would rent out regiments or whole armies to other nations during this era). Having experience would make it easter to get one of the available positions, especially if you did not have as good contacts as any of your potential rivals.
Soure: Svenska knektar: Indelta soldater, ryttare och båtsmän i krig och fred (Swedish man-at-arms: Alotted soldiers, cavalrymen and sailors in war and peace) by Lars Ericson Wolke.
As a follow up, let's say I'm in China and the Qianlong Emperor is organizing another war with some barbarian group or another, and I've decided to join the military. How would being a person of some stature affect my future military service?