That's rather an open-ended question. Covers a lot of ground. I'll try to give it a shot, though.
As far as a combination plinker/hunting caliber is concerned, .44 Magnum would make a good, all around choice. More than adequate as a short/medium range hunting caliber. Factory ammo is easy to source. A versatile and easy to reload cartridge. Most brands will also accept .44 Special cartridges. A good choice for low recoil target shooting.
Brand wise: That's going to depend on your budget. Plus, which one you like best. Handle each make first, if you can.
Top of the heap(in .44 Mag.) is the Miroku-Winchester Model 1892. Excellent build quality, accurate and reliable. Next, Marlin, Henry and Rossi. All are good performers. Henry in particular, has outstanding customer service.
If you want a simple, dependable and easy to maintain rifle, either Marlin or Henry. These two rifles are essentially identical internally. Both very easy to strip and clean, etc.
Rossi rifles may not be as well finished as the others. But, are certainly reliable, durable and accurate. The Model 1892 being very popular with many shooters.
There's likely others I've missed. But, this should offer some ideas.
Al
ps : Calmcat: The Henry Big Boy is an excellent rifle. With .357 being a versatile choice. Perhaps lacking the punch of the .44, but still capable of taking deer-sized game(where allowed), at close, woods ranges. I am not a fan of the big loop lever, My own personal preference being for the original 'small' lever models. But, for winter use wearing gloves, the extra room is welcome.