The brand or style of the bike doesn't matter as much as the condition of the bike. There are plenty of used bike buying guides online that should tell you what to look for.
If you want to go new, for $300 you could get something like a Giant Boulder new from a bike shop.
http://www.giant-bicycles.com/en-us/...er/7305/44110/
I'm not as familiar with the offerings of other brands, but trek, specialized, scott etc. should all offer something similar. If you buy from a bike shop, find one that offers free tune ups at least for the first year.
Stay away from department store/walmart bikes.