Congrats on getting your PAL~now the (safe) fun starts!
If you don't mind me saying...it sounds like you might be getting WAY ahead of yourself. I suspect lots of guys on here (like myself) have been shooting since well before they maybe should have
and evolved into their current sensibilities having spent allot of time with sling shots/air guns/22s before even CONSIDERING centerfire rifles or shotguns. At least I did. I would hazard a guess that by the time I'd even fired a shotgun, I'd put 10s of thousands of rounds through air guns alone, thousands through 22s, etc. Didn't even know what and FAC even was...not sure they even existed back then!
Anyhow, what I'm trying to say is this~doesn't sound to me like you need advice on the best caliber/gauge, rather, what you need is a decent 22, a crap load of ammo, and some safe trigger time under the guidance of someone you trust. I still thoroughly enjoy that sort of thing at my age, but felt with that experience behind me, I have a sense of the kind of rifle I want to carry, shoot, @ what distances, what kind of optics make sense. With shotgun gauges~I shot old farm guns forever before buying my first 870 pump. Shot some skeet, but mostly trap for YEARS before I even felt the urge to hunt with it. While I don't think you need several decades of plinking, target shooting, tons of trial and error...I DO think you should maybe slow down a little and get comfortable with a less powerful caliber, get lots of practice, and enjoy the process. I think if you do, by the time you buy your first hunting rifle...chances are it'll be a good choice, one you're proud to own, and one you're probably going to shoot a HECK of allot better.