@James Lanier If you're asking about private lenders (individuals instead of banks), you'll find that it's relationship based and you'll really need to have your ducks in a row and show them that you have a plan for the property and some experience rehabbing.
The bigger the project, the more they're going to want to see that you have experience doing a project of that size. And just like with banks, the ideal time to approach them and build the relationship is when you don't need the money.
Also you mentioned starting your real estate ambitions. Do you have experience doing a major rehab? Every property I've seen in the last 5 years in the 40-60K range needs significant work. That's fine if you've done projects like that before, but I'd be very hesitant to say start off with one of those if you haven't.
You'll also find, if you haven't already, there there is a lot of competition in the under 100K price range so often those properties are getting bid up to almost unprofitable levels (unless you already have a crew and are trying to keep them busy). On the other hand, if you intend to buy and hold the #s may make more sense for you.
To your main question, there are lenders, but every one I know is going to insist on being in "first position" (i.e., being a first mortgage). So if you're buying in the 40-60K range you'd need to pay cash for that.
If you can do that, then yes, you can probably find some lenders who will give you a loan to do the rehab, but they will likely give it to you in construction draws, meaning you will have to pay for part of the rehab, then they will reimburse you for what you've spent and add to the loan balance.
Your best bet for financing a project like this, and you may even find some willing to give you a 2nd position mortgage (allowing you to fund part of the initial purchase with a loan), is family and friends who already know you and are willing to help you out. They may want to do so as loans out of self-directed retirement accounts or they may want to be equity partners (i.e., co-owners) instead; that's a negotiation based on your relationship with them.
A 203(k) loan (i.e., bank financing) is a good idea, you'll always get the best rates from institutional lenders, but there's a lot of paperwork and delay, and most of the offers in the sub-100K range are cash offers so there's virtually no way your 203(k) contingent offer is going to be accepted - unless it's a deal you find yourself that is not on MLS and you're dealing directly with the seller, which is by far the best way to find a "deal" in real estate.
(It's also, not coincidentally, the most work to find and create, though you can give up some margin by carefully buying such a deal from a wholesaler, after you vet that it really is a deal - many I get presented from "wholesalers" are not in fact deals at all.)
Somewhat ironically, you may find you have better luck with a 203(k) loan buying a fixer-upper from the MLS in the higher price ranges since fewer rehabbers look there and there's less of a chance you'll be competing with an all-cash offer.
Good luck, and let us know what happens of course!