I would say that most of your budget rifles today, are quite good; except for remmy. any under 400 bucks, Wetherby, howa, savage, stevens, marlin, thomson/center's new one,mossberg, smith/wesson; will all give good performance, and low cost. all around, the best all around cart is the 30.06, but it does have some kick to it. 308, 7.08 and 270 is a bit less,25.06 a bit more less, and the 243 is less than that. Anything between 243, and 30.06 is just fine for deer, but if yo ucome across the occasional mule deer, elk, black bear or such, I myself would like to be carrying the 30.06
Your scope, is actually going to be a more important choice, than the list of above rifles. it should be clear, focus very well, and take recoil. For a do it all scope, that won't break the bank, think Nikon, or burris.
if the rifle you choose comes with a scope, that is fine, try it out. but if it loses zero, moves reticles, or is not clear or crisp, when you put it on it's highest power setting, then get another scope.