In your lower price range I really like the Weatherby. I got a Vanguard Series 2 in 243 Winchester and my first three groups were 1", 3/4" and 3/4" using handloaded Barnes 80 grain TTSX. Tough to beat that for the price.
I'll be scolded for this but I just don't like the looks of the Thompson, Tikka, and Savage rifles. From what I've read and heard they are shooters but I have to like how it looks when I'm putting my money down for it
A really nice point about the Remington 700 is just about everyone makes parts for them. Buy a cheapy ADL from Walmart for $400 this year and build it into the custom rifle you want over time.