Hard to beat the great ol' 30-30 in a lever action rifle! Low recoil, effective on the game you've mentioned within the range you've mentioned, and is light, handy and fun to shoot!
But definitely lots of choices as previously mentioned; 250 Savage, 257 Roberts (not mentioned but was made in limited numbers in the BLR), 7mm-08, 284 Win, 308 Win, 300 Savage, 303 Savage, 30-40 Krag, 30-06, 348 Win, 35 Rem, 356 Win, 358 Win, 375 Win, 444 Marlin and 45-70. There are many other less common cartridges also chambered in lever action rifles
Open sights vs scoped is going to be as big a factor for your preference as the the make and model of the rifle.
Marlins (except for waffle tops), Winchester AE's and Model 88's, most Henry's, most Savages, the Sako Finnwolf and the Browning BLR's are easiest to scope. Winchester and Browning Model 71's will be open sights or peep sights. Sorry, do not recall how easy it is to scope a Winchester 1895.
In the end, it is a very personal preference that only you can decide.
As for something classy and will be as much fun to just hold and admire or polish in front of the fire on a cold winter's evening, the original Winchester Model 71 Deluxe, or the fancier newer Browning Model 71 High Grade Reproduction from 1989 (limited production in both rifles and carbines) may be to your liking.
The Sako Finnwolf is a fairly rare rifle and was offered in very few calibers, so one in a 308 Win may be interesting to you.
Turnbull is making some very fancy lever actions, as is Bighorn Armoury. These may be of more interest to you. Definitely not inexpensive firearms!
Many lever actions were also made available in pistol cartridges, and a matching pistol/revolver and rifle may be more in line with your desires; many options there too!
Best of luck in your quest!