If you're going with Remington I'd recommend you stick with a model 700 SPS. If it don't have to be Remington I'd suggest a Marlin XL-7/XS-7, or a Savage Edge. Both can be had for about 300$ sans scope. PLEASE do yourself a favor and stay away from the model 770. The 770 is simply an "improved" model 710. The 770s are a lot better but the 710s were junk for the most part. I used to say there were 2 kinds of Rem 710 owners-those with broke rifles and those with future broke rifles.
Sometimes you earthlings REALLY amaze me!