A 203(k) loan would be the way to go to buy a home and include within the loan the money to do the repairs. But someone familiar with mortgages will have to address the low amount to be borrowed.
And while it probably would be easier going above $50,000, don't spend more just because it'll make that part of the process easier. If you can get the property for $20,000, why spend nearly double that ($35,000, assuming the more expensive home still needs repairs)?
There are a couple of other ways to buy such a low-priced property. If it weren't a foreclosure (if you can find someone just willing to sell to you directly), you can look for owner financing. Another option: Find an investor to buy the property, then sell it to you on terms. The investor will make some money--so it'll be more expensive than if you'd bought it directly--but you will be able to get financing. And it can be structured so that your payments are still reasonaable.
Yet another option would be to get a personal loan. The interest rate would be higher, but that could cover part of the expenses. Or get a co-signer for the personal loan.
Hope that helps.