I've seen some mini14s that shoot well, I've seen more that don't shoot well. If I were you I'd be looking at a Savage 10 or 110. I'd be looking at a .243 for your varmint/deer combo. For glass a mid level Nikon or Leupold and you'll have some money left over for ammo.
That howa would def be a nice rifle. There are a ton of rifles under your budget though, including some very nice ones. I'd go to a big shop and look at a bunch of rifles. Narrow them down to what you like and what feels good and then do some research online and shop around for the best price.
-Jake