Regards the Remington 700, forget about the supposed trigger problems. If there was an issue, it's long since fixed.
The flawed trigger design was replaced in 2007. New rifles should be fine. Rifles made prior to 1982 are more likely to cause problems, but even then it is rare, but very real.
Personally with your budget I'd be buying a Winchester. Get the Featherweight if you want wood, the Extreme Weather if you want synthetic. But that is largely personal.
There isn't enough difference in 2013 to matter between 270 and 30-06. In 1925 when the 270 was introduced they were loaded much differently. Today the best 30-06 loads shoot 150 gr bullets 300 fps faster than 1925 loadings and will all but match 270 loads in trajectory. With modern bullets a 150-160 gr 270 will kill the largest animals in North America with ease. Between the 2 I'd pick the rifle I liked best and not worry about which of the 2 chamberings were stamped on the barrel.
The scope is an excellent choice on any rifle or chambering.