Remington's quality control has been hot and cold (mostly cold) since the Cerberus- Freedom Group take-over (although it wasn't particularly great before, either). I have had examples where the scope mount holes were drilled off-axis (requiring nearly three turns of windage on a scope just to zero) and other assembly issues.
The 700 Varmints and Senderos in H-S Precision stocks were a very good value, and with a little trigger work and good optics perform very nicely. You can also buy them with wood or junior-length stocks.
For gals and slight builds you can't go wrong with the Varmint profile barrels in calibers from 243 thru 308. In a long action the 7mm (especially if you add a muzzle brake) tame that rifle to where it won't make them develop a flinch.
I'd recommend the 243, 260, and 308 for all-round use. Not too expensive to shoot, not abusive as far as recoil, and not too bad hauling into a blind. They might be a little on the heavy side if you do a lot of foot movement, but if just trekking from the truck, off a horse, or off a quad they're not ignorant.