I was recently looking for a "budget" deer rifle for this deer season. Local hardware store had a variety of budget deer rifles in stock included Remington 770, Savage Axis, and Ruger American. Of those I liked the Ruger American the most. My choice though was a used Savage 110 in 270win they had for $275 with a Tasco scope. I had it out to the range this week, and I have to say it's a decent gun. So my recommendation would be a used 110 or the Ruger American.
"The rifle itself has no moral stature, since it has no will of its own. Naturally, it may be used by evil men for evil purposes, but there are more good men than evil, and while the latter cannot be persuaded to the path of righteousness by propaganda, they can certainly be corrected by good men with rifles." Col. Jeff Cooper, from The Art of the Rifle