Where and what deer are you hunting? I lived out West for several decades - that meant mule deer and possible long shots. If you sit in a tree stand in the woods waiting on a small white tail to show up, your needs will be different
I have an older 700 BDL in 7mm mag - great for Western hunting of all 4-legged critters with horns. I also have a Model 7 in 7-08 with the 18" barrel - perfect for climbing a lot or where shots and animals aren't as far away or as large
White tails - anything in 243 and up - look at Remington, Savage, Browning, maybe even the new Winchester. You might also find a SAKO or Tikka used in your budget
Mulies - I would start at a 6.5 x 55 and go up from there
Proper bullet type and placement are more crucial to success than cartridge size