Mosin Nagant. damn near hard to beat a $100 rifle.
Big 5 is ripping people off. pre-sandy hook they were asking $229 for a Mosin.
here's a place you can get Mosins for about $100.
http://www.classicfirearms.com/c-r-eligible/lng-m91-30-nagant
I've bought quite a few things from them, they sell very high quality surplus guns.
H&R Handi Rifles aren't bad, mine's pretty good, although I've never really cared for accuracy... I'm not hunting with mine, I shoot extremely powerful experimental ammunition in mine that is so powerful accuracy is not important. There's complications measuring MOA anyway, if it was in a reasonable caliber like 30-06 or 223 it would be easy. But no, mine's in 500 S&W Magnum which results in 1/2" holes in the paper and a 3 or 5 shot group results in huge holes that means measurements difficult. I'm guessing its a 2 MOA rifle...
Savage isn't bad, but for $300 limit you won't manage anything better than the absolute super-basic Axis which IMO is a poor deal. you can't rebarrel, it comes with a Sporter barrel that makes it unsuitable for anything else besides hunting, and there's no options for customization of any sort. no free floating of barrel, no custom stock, nonadjustable trigger, so unless you have no plans on upgrading later it's really a bad deal. spend $100 extra, buy a Savage 10/11/110/111/12 or 14 rifle that can be modified as you need later down the road.
You might find a used rifle (Winchester, Remington, Savage, Stevens- just about every rifle brand that exists) in your price range and in a suitable caliber, although i haven't checked the market right now, i imagine the choices are limited. maybe later after the panic is over you'll find some good deals.
used rifles typically pre-1970 is very good, they were all steel and wood back then. 270, 308, 30-06, 8mm, 7mm, 284, etc.