Yes, your credit score is not all that bad. As long as you do not have any recent evictions, bankruptcies, etc. you should by ok. As a rule your income will need to be 3 to 4 times the amount of the rent (If rent is $700 your monthly gross income should be $2100 - $2800). The key is having all your documentation too (check stubs, bank statements, etc.).
A way to show you are serious if you have not so good credit is to have letters of explanation attached with an application that will explain why the blemishes are on your credit. Have a clean car when you go look at the homes. Dress nice and present yourself as if you were meeting the President...you should do fine and have a place in no time.