welcome to the shooting community, and welcome to muzzle loading. I would get a .22, which is inexpensive to shoot, and is a good platform from which to learn basics like sight picture and trigger control. You need not spend a boatload of your hard earned, over taxed God- entrusted dollars (unless you really want to), and a modest little .22 will give you many hours of relaxation and enjoyment.
when my children were getting to the age where kids need to learn how to shoot (as I told both my girls: never really trust a man who can't ride, can't cook, or can't shoot: there's probably a bunch of other stuff he can't do very well, either. ... thought my wife would swallow her tongue) i thought of going right to flintlocks, but decided against it, and went the .22 route... glad i did. it turned out that neither of them really caught the shooting bug as I did, but they now can shoot adequately, and if I'd insisted on a muzzle loader, I'm afraid the learning curve would have spoiled it for them both.
Now once you're comfortable with your .22, you should look at a muzzle loader, because cool guys shoot muzzle loaders, and you do want to be cool, don't you? Sure you do!
If you have patience, and you want to have fun, i would recommend a caplock. If you have LOTS of patience and want to have LOTS of fun, try a flinter. Flintlocks are harder to shoot, require more finesse, need more careful attention: flint condition, priming, frizzen, all that sort of stuff. But once you get a flinter up and running, they're a bunch more fun. (mind you, this is just one guy's opinion, and no doubt worth what you just paid to get it.)
If cost is an issue, you should take a look at either a Lyman GPR (Great Plains Rifle) or a Thompson Center in one of their several "Hawken" patterns. Neither of these guns is what you will see referred to as HC or PC (Historically Correct or Period Correct), but either will give you excellent value for your money. I still own the Thompson Center that I bought in the early eighties, and it's served me well, and will serve my heirs as well. You will find some good bargains on the Classified section of this website, by the way. Most likely you'll end up with a .45 or .50 caliber, since these are the most common calibers for factory built rifles. If you 'take the plunge' and have a gun built, or build one yourself, you can of course get any caliber you want.
For now, however, I would recommend a .22. Don't forget a few bricks of decent ammo, a cleaning kit, a case, targets, a good staple gun, a roll of duct tape (I'm in Vermont- we never go anywhere without duct tape), and whatever gunlocks or safety stuff you local laws mandate.
By the way, you should (if you haven't already), join the NRA and the NMLRA. Again, what groups you join is ultimately up to you, but they do stand up to those who would repeal the Second Ammendment and confiscate the entire contents of our gunsafes.
Good luck, and make good smoke!