Not having 20% down does not have anything to do with your credit score - but it will have something to do with the kind of loan and interest rate you will get.
Your current credit score plays into buying land or a home.
After the purchase your debt to income ratio will change and may play into any other loans you might want to take out after that.
What to do while you look to the future home buying . Make a budget - track your spending. Save for down payment, closing costs, utility deposits, moving costs, repair/renovation costs, decorating/furniture/appliances, yard items/tools & miscellaneous.
AND after all that - have an emergency fund in place - you need one when you are a home owner .
Buy a house you can comfortably afford. 25-28% of your TAKEHOME pay . That should cover mortgage+PMI (if not putting down 20%) + insurance+taxes+utilities. More than that can make you house poor.
Pay off your consumer debt , save, save, save - meanwhile .
Make a list of needs for a home, and a list of wants. Know what you are willing to compromise on as you will not get it all.
Two good books to read: Homebuying for Dummies and Mortgages for Dummies.