As the title says, would the GURPS system be a good choice for a non-magic campaign that has a tech level roughly equivalent to earth Europe's 19th century and a focus on roleplaying rather than fighting?
I am looking for something with well defined rulesets about guns and other firearms, how armors work against these, as well as how wounds inflicted by them would behave. I am looking for a non-level-based system as I don't plan on basing the campaign around encounters (as I would with a classic D&D campaign).
The aim of the campaign is (at least in the beginning) to give a few friends that have never in their life played a pen & paper roleplaying game some introduction to it with a focus on the roleplaying aspect.
For the first few sessions the campaign will have a military setting. The players will work their way through 'military academy'/'boot camp', being led through exercises such as hand-to-hand combat, firearm usage, as well as different skilltests (such as repairing a weapon or machine, playing cards against NPCs, etc..) – in order to give them a feeling for the different aspects of roleplaying games and how they play.
The world in which it plays is an imagined world, based on the physical rules of earth and having a technological development closely aligned to earth's.
The campaign and portion of the world which it will play in will be most similar to 19th century Europe and the rest of the Western World.
The 'military academy' setting is chosen as such in order to provide a narrative/storyline similar to what they know from computer gaming.
The 'academy'/'bootcamp' theme is meant as a means to introduction (as its purpose is in real life) – if they happen to like what they find I plan to throw them into a theatre of war rather quick
GURPS is a pretty good ruleset for the kind of game you describe. It's got good rules for pretty much everything, and the pointscale that the system is built on works pretty well for a game where it's assumed that people will have guns.
I'll go through each of the requirements you list, and how well GURPS deals with it.
"roughly equivalent to earth Europe's 19th century"
GURPS has a Tech Level system. One of the levels is TL5: The Industrial Revolution. This tech level deals with stuff from the early 1700s to the late 1800s, so most of the stuff you're looking for will be TL5. This includes breech-loading guns, ironclad warships, hot-air balloons, steam engines, and the like.
"a focus on roleplaying rather than fighting"
GURPS is pretty flexible when it comes to the roleplaying/rollplaying continuum. There are many, many skills that deal with the various ways you can interact with people, and there is quite a bit of detail given to interpersonal interactions. It's not as mechanically rich as the combat, but the rules are there.
"well defined rulesets about guns and other firearms, how armors work against these"
Here's where GURPS really shines when it comes to what you're asking about. For any given topic, there is almost certainly a GURPS book about it. What you want here is GURPS High-Tech. There are pages and pages of descriptions of various real-world armors and weapons, including notes on how it was actually used in combat. There are rules for different armors for each hit location, and pretty much any kind of gun you can name. The rules for how guns and armor interact are pretty simple: armor reduces the damage done by a weapon directly, whether or not it's a firearm.
"how wounds inflicted by them would behave"
It's not terribly clear to me what you want here, specifically, but GURPS generally has a pretty simple wound system, with extra complexity that you can add. Typically, you just take damage off of your hit points, and that damage heals with time. If you take too much damage, you suffer some penalties. If you take damage that is specifically to an area other than your torso, you might take some special debuffs, like getting stunned from a head blow, or a crippled hand. There are also rules for how wounds can get infected, and how aftercare works.
That said, GURPS is pretty realistic in one way that makes it extremely unfriendly to new players: GURPS combat, especially with guns, is incredibly deadly. For example: TL5 rifles deal between 3d and 5d damage, usually of the pi+ type. That means that a hit does about 14 damage, and any of that damage that penetrates armor does 1.5X the damage roll. Typical infantry armor in TL5 gives DR of 5, which means that a typical rifle shot will deal 9 pi+ damage, which works out to a total of 13 injury. Since the average GURPS character isn't likely to have more than 15 HP, this means that a slightly lucky shot will leave a character down for the count in one hit. This realistically reflects how deadly combat is in real life, but may not be conducive to a fun first game for new players.
"give a few friends... some introduction to it with a focus on the roleplaying aspect."
This is one place that I don't think GURPS does very well. GURPS is not a great system for new roleplayers. One of the problems with GURPS that makes it an unpopular system is that it's exactly as deep as you want to go. If you want specific hand-to-hand fighting rules that feel just like an actual martial arts fight works, then GURPS can do that. IF you want to just roll some dice and do some damage, GURPS can do that too. The problem is, since the books don't make it obvious what parts are important and what parts can be tossed, it's intimidating for newer players who are trying to get to that second level of system mastery, where they can learn and know rules without asking their GM.
If you don't expect you players to have to know any of the rules beyond a surface level, then GURPS is just fine for new players. If you want them to make that next step up, and start being able to make their own characters and generally know how the rules work, GURPS may be a little intimidating and difficult to use. The best and worst thing about GURPS is how complex it is. When it comes to teaching new players how to become intermediate players, GURPS's complexity works against it.
Your boot camp idea seems solid, and is an interesting way to introduce them to how the rules work. I've run military games in GURPS before, and the system works pretty well at that kind of thing. As long as you're okay with how deadly GURPS combat can be, and are willing to help you players a lot once they are interested in more than basic system mastery, GURPS is likely a good system for you.