Search properties and email each agent about your situation and details. Some of them will respond with information about how to proceed with sending an application so they can review it and answer your questions.
You should be able to find a property to lease. I tell my clients to think of a rental application like a job resume - it is the first impression the landlord will have of you. Make sure it is neat and complete. If you have a strong rental history, see if your current landlord will write you a letter.
Some landlords will have a credit requirement and some will not. A 20 year old felony will probably not be a problem unless the community has a strict no felony rule. You should be able to find out requrements before going through the application process.
A lot of times the main thing landlords look for is rental history and the ability to pay the rent each month. They like to see three times the rent amount as income. Many will work with bad credit with a larger deposit or a lease guarantee (similar to a co-signer).