On that budget, Styer Pro Hunter SBS (Safety Bolt System) "Mountain". Going for $799 or a tad less NIB down this way. Has a 20" barrell, a stock that can be adjusted to 3 lengths of pull by removing spacers. Excellent safety system. It is on the pricey side of the factory rifles, but I cannot imagine any being any better a shooter. I have several others ... have helped sight in many otehrs .... too many to mention. I have 2 Styers .... 30.06 Spr. and 308 Win. Both have a very good trigger. Excellent accuracy. I have hunted with mine in -30F(dang Montana !!!) to 100F (dang SE Alabama!). I have had zero issues with mine and highly recommend this rifle.
Having said that I bought my niece a Browining AB-II and my grand daughter a Ruger American in 270 Win. Neither is fsancy, but both shot great. Lot less $$$ !!