Ok, I'm a professional photographer, so here's what I'd suggest:
Shoot film. You can't properly equip yourself digitally for less than $2,250... and that wouldn't leave money for memory.
Go buy a used Nikon F100 and a new Sigma 70-200 mm f2.8 HSM EX lens. Also, get a 2x teleconverter.
You'll be in the $1,250 range.
In order to shoot wildlife, you'll need a "fast" lens. (When discussing lenses, "fast" means a large aperture or opening - like f2.8 - smaller numbers mean larger apertures.) You'll need this large aperture to shoot successfully in the low light conditions that you'll encounter in the woods, esp. early and late in the day.
BTW, if you want a head/shoulders shot of a deer at 100 yds, you'll need a 500 mm lens and even then you'll have to enlarge and crop the heck out of it. A 400mm lens will give you a field of view of about 10 yards wide at 100 yards. (I don't have a 500mm, so I'm not sure what the FOV would be.)
Bad news: there's no way you'll want to spend the money for a 500mm/2.8 lens. A "cheapie" 500mm/4.5 lens is around $3,300.