Sadly, I cannot offer a definitve answer to this question because banks all have different lending practices, and all of them are tighter now. Some will give those with lower credit scores (in the 500-600 range) a chance, with a higher interest rate, but many require a cosigner at that FICO score these days.
For a sub-prime mortgage rate, you'd likely need at least a 700, which is nearly perfect credit. Don't quote me on this, as my mortgage lending experience is a bit dated. I have recently tried to get a mortgage with a lower end score, and was unable to do so all together due to the lack of a cosigner.
If high interest rates are a concern, be prepared with a higher percentage down payment--around 15-20% and/or a cosigner with a good score. You can shop around without damaging your score if you place all inquires in a 14 day period, but don't go too crazy.
Hope this helps! Consider asking a few banks what their minimum credit score is for a rate you like--and this should help you, provided you know your own score. If you need to check your score, you'll need to pay a fee, as the score doesn't come with the free annual credit report.