I would have to agree with the majority here. The '06 is the most versatile and available round around. You can get the ammo fairly cheaply and also with a huge range of bullet configurations. Coyotes to elk.
As for manufacturer, the Remingtons are always great, but I have a beat up old Savage 110 that has taken a beating and it just keeps on slinging them out there.
$500 is doable for a nice rifle but a good scope will run you a little over.
I would also like to suggest a 25-06. They shoot very flat, very fast and have considerably less recoil than the 30-06. Depending on what the terrain looks like, I think it's a great gun for Oklahoma and it is actually fun to shoot.
The 94/22 will get the most use. How many 22 rounds have you shot in the last year? How many centerfire? You can have a LOT of fun with the 22 without breaking the bank.