The Savage Axis has been mentioned already,it has gotten a good share of the economy rifle market. You can get one for about $300,sometimes with a cheap scope that would need eventual upgrade. The Marlin XL/XS 7 is a pleasant surprise to most people looking for a $300-$350 rifle. What you want to stay away from are the Remington 770 and Mossberg ATR, they both use cheap stocks and have bolt cycling issues. Maybe best bang for the buck is a Weatherby Vanguard Series 2 for about $500-they have upgraded stocks,a new adjustable trigger with a 2 stage option,3 position safety and a Sub-MOA claim from the factory using recommend ammo (your results will vary depending on your ammo choice).
Walmart sells both a Savage 10 FPX combo and a Rem 700 ADL (no scope) with X Mark trigger for about $425-$450. Both have good reputations in the field. Cabela's sells a 700 ADL for about same. T/C Ventures go for about $500,may catch a sale for $50 off-solid newer design,similar to the Axis.
Ruger also has an economy rifle called the "American" that should be $450 or so,again using a lot of the features seen on the Axis,T/C,even Tikka T3,but seems to have some unique stock/action blocks for stability and a little Browning A-Bolt and Tikka DNA in the features.
I like the idea of an Axis in 223 or 22-250,not so much 30-06,which is what you should consider as your cartridge choice. Yea,I recommend looking hard at the Vanguard-even in base model it is solid.
I own A-Bolts and have used CZs,Rugers,Colt-Sauer, others; like the A and X Bolts,CZs are like bank vaults.