If I only could have four it would be:
Springfield XD9 compact
Ruger 10/22 (or Marlin model 60)
Walther P22
FN-FAL
Why? One training rifle that also makes a great small game gun, one training pistol that's also a minimalist concealed carry pistol, one defensive handgun, and one defensive rifle that can also be used on big game (with a 5 round mag). Of course, I'm not a bird hunter, so YMMV.
Depending on what part of the country you live in and what big game you see and at what range you find them, I'd opt for either a 30/30 or .44 magnum lever action or a bolt action .270, .308 or 30-06. If you live in brushy country with smaller deer, no elk, moose or big bears, a .44 or 30/30 seems adequate out to about 75-100 yards. If you have larger game with longer shots out to 200 yards or more, you'll want a semi-auto (Browning BAR) or bolt action (Remington or Savage) rifle in a heavy hitting caliber.
While I like the idea of .357 lever actions, I just don't think you're gaining a huge amount over your existing 627 (yes, it will be more reliably accurate out to 75 yards, but you're already good to nearly 50 yards with a long barreled 627.