You really should start working with a Realtor now to begin receiving email updates with homes that are in your price range. but before you do that, you should speak with a lender to see exactly what it is you qualify for. It's not just about a credit score, you will have to provide pay stubs, credit obligations, legal judgements, etc, to the lender so they can see how credit worthy you are.
Once that is done you will have an amount that you qualify for, which will help both you and your Realtor search for a home that is within your price range. Even if you found a house today and had an offer accepted on it, it will most likely take 45 - 60 days to close on it. So it will take time even if you act quickly.
I would get prequalified immediately, and if your credit needs some help, they can tell you what to do to help you improve your credit worthiness, such as maybe paying off a credit card, or consolidating some bills, etc. So if you are set on purchasing a house, get started today.
With rates as low as they are these days, chances are your mortgage payment will be less than your rent payment. Plus with the competition on buying homes these days, there are no guarantees that you will have an offer accepted quickly. Most of my clients have to place multiple offers, many over asking price, in order to secure a home, it is that competitive these days.