This is a great question. The important variables besides your price range are the condition of the property, your credit score, and your personal financial situation. With an experienced realtor and a strong mortgage broker to help you, you will be able to determine how many options you have an choose the right one for you.
For instance, I am working with an investor now who had to pay 100% of the purchase price at auction for a property that would have been impossible to finance through FHA, due to issues with the property condition.
With a property in FHA-acceptable condition, you could make a downpayment as small as 3 1/2 percent of the purchase price. For people who understand the limitations of the 203k loans and properties needing relatively minor work, the 203k and FHA financing products can be productively combined. The details are important with 203k because licensed contractors have a window of time to complete renovations and there are limits on the amount of the 203 loan.
Please feel free to contact me for the names of experienced loan officers who understand the 203K loan process. For more information about the process of buying or selling property, please visit my blog.
Good luck in your search!