Running does use different muscles than riding but conversely the same applies to a runners attempting biking. I ran alot but turned to biking due to running is actually bad for your joints from the impact. I have lower back issues too from over 20 years of serious weightlifting. Biking has given me a great cardio outlet and a means to lose serious weight.

Your doing the right thing by switching to biking due to alot less to almost no impact on the knee's for sure. Your feet will love you too. I know this statement will tee off the runners here but it is a fact. Sports medicine doctors all say the same from my experience. Let's face it, your trying to exercise your heart point blank. Why ruin your knees and feet in the process.

I am not saying biking does not have it's drawbacks too but not near as much. I find biking is hard on your saddle and at times being bent over my back locks up but not like it did running.

If your budget is $300 I suggest too looking used. Great used bikes out there because bikers tend to keep their gear in great shape. Try the classifieds here and on mtbr and craigslist and I am sure you will find something to fit your needs and budget. If your 5'3" I assume you would need a small frame bike for sure. Just an assumption.