Your question is way too vague.
"Woods" can be in Arkansas and in Georgia. They can also be in Wyoming or Alaska.
Arkansas and Georgia have no Grizzly bears!
However you may have a run-in with a 2 legged predator in the south more often than you would in Alaska or Wyoming.
Protection from what?
Secondly, bullet weight is only a small part of the question. How about bullet construction and bullet shape?
Again, the question is "What is the target"?
A 225 grain Hollow Point is vastly superior for defending yourself against human predators compared to a 360 grain round nose. But a 335 Grain LBT Flat nose is going to be a LOT better than a hollow point if you need to shoot a large bear, a moose, a buffalo, and so on. If you get an LBT flat nose over 1250 FPS it will make as large or even larger a hole in flesh (cavitation) then most hollow points and do it about 400% to 500% deeper.
Again, what do you need to shoot?
What I recommended as an "all around load" (when I was running cast Performance bullet Co I got that question probably 20 times a week) is a 325 grain LBT Bullet at about 1200 FPS zeroed at 50 yards. That load leaves 1.25" permanent wound channels through flesh and bone, and will shoot clear through a large elk from a quartering angle. In most Ruger revolvers it also will shoot 50 yard groups of 2 1/2". That would do for killing a bob cat, and also is ok for a mad moose. The only down side is that you MUST know what is behind your target because unless it has tracks on it, the bullet is probably going right through it.