Uncle Duke, I'm sure you know this, but let me be more specific for the benefit of our new shooter.
If you want to shoot .22 and shotgun, you could buy a Savage over-under, .22/20 gauge gun that would do both jobs. I've owned one and I loved it. But now when I want a shotgun, I use a nice 20 guage pump or 12 gague pump depending on what I'm looking to shoot.
Sure, I could shoot trap and skeet with a Savage combi-gun, but it would be foolish. Extra weight, bad ergonomics ect. I could take the same gun shooting targets with the .22 and I have the same problem, extra weight for no good reason, single shot, break action... slow to work and cumbersome.
Likewise, a NEF rifle/shotgun/muzzleloader will do all the things I want with different barrels, and the ergonomics aren't bad. The gun will be too light weight to make shooting 12 gague comfortable, and way to expensive to use as a .22. These kinds of guns are great in countries where you can't own several guns. If you can only own one or two, you buy one that can be a shotgun, rifle, muzzle loader, turkey, bear, deer and hummingbird gun. (JK about the hummingbirds... I use pellet guns for that
On the other hand, get a decent .22 and use it to learn to shoot. Great for plinking and target shooting. More than one person has used one for defense in their home though I don't recommend it. That's $150.
A decent used shotgun for skeet, birds, deer in Mass, home defense, rabbits and ducks is great, but not so much for target shooting bullseye at the range. That's about $150 for a used Mossberg or even a Remington pump if you look hard enough.
Then for under $100 you can buy a Mosin Nagant centerfire surplus rifle that does all the things other medium game size rifles do, for far less money. It's also a great gun for defense in case of SHTF. Good for up to deer size game, and fun at the range. Plenty of power, and the ammo is relatively cheap.
After 50 years of shooting, while I have way too many guns, my basic battery would include a good .22 rifle, a decent 20 or 12 gague pump shotgun, a good quality lever or bolt action gun in .223, 243, or .308. I'd also want a good .22 pistol and a .357 pistol like a Ruger or a Smith.
After that, almost everything is a sub-catagory. You get into big guns, little guns, pretty guns, scuffed guns you don't care about dropping on the rocks, big shotguns for geese far away, small shotguns for woodcock, big center fire for elephants and Zombies, medium center fire for small game, small centerfire for varmints and target accuracy, and of course on big motha just to have to show you are tough.