to add to
Clout $ Monei 's post.
Getting a firearms license will in most EU countries also require a mental health check up, a criminal record/background check and a guns safe to keep your guns in at home.
The specifics of these vary but in general you get to pick your own doctor or shrink to sign a bit of paper telling the police you aren't a lunatic or the sort of guy that's looking to suck a load of buckshot trough his brain.
You have to present the cops with your criminal record (that they keep, just a stupid nuisance tax) and they get a couple of months (and they won't rush it trust me) to figure out you aren't a wanted criminal ect.
The safe is kind of self explanatory but depending on where you live it may have to be bolted into a wall and you'll have to have the cops check in on it. So yay cops coming over for thee. Better have a vacation day left over because they will only come during business hours and they probably won't give an exact hour.
I'd advise anyone that wants to start out by getting a hunting license. You don't have to do any of the above to take a hunting license exam it's self and you can hold a hunting license without getting a gun.
Hunting is a great gateway into the wider gun owning community. Also since hunting tends to be a more upper middle class hobby in (Western) Europe you will get to know everyone some useful people that way. Lawyers you can ask for advise over sip of brandy, a doctor who also hunts and is generally positive towards gun ownership, where to buy your gun safe and who will install it right so you don't have to deal with a repeat visit from the cops ect. Also knowing a doctor never hurt anyone.
Getting a sports liscense will in most countries require you to go shooting x times per year with those guns you've got under that liscense. Try to spread those out, December can be a very bussy month at the range.
The next thing is that you will have to renew your lisence in most countries.
Same deal overall get a mental health check and background check by the cops (agains very much a nuisance tax especialy since if you've done anything that merits them not renewing your liscens they'd have taken your guns already).
Getting your liscense renewed is a bit of a pain in the ass but aslong as you don't try to get it all done right on the dead line it shouldn't be a problem.
Collectors lisences isn't something you can get as a first time owner in most countries and they'll require you to aleady have several firearms before you can get one.
CC permits are very nation specific in how to get them and if you can get one. If you want to get them I'd strongly advise you to speak with a lawyer that knows your countries gun laws well before you try to get one.
Make sure to know what constitutes legal self defense in your country including the case law.
Owning can be a bit of a hassle but it has it's own rewards like americans laughing at you until the heat death of the universe.