I believe W L is correct that you only have to be under contract by 4/30. There is absolutely no chance that you will close on a house by 4/30 unless you have it under contract right now.
Getting a REO under contract by 4/30 will be a challenge.
You have one huge advantage over investors - you're willing to pay more. An investor needs to get a very large discount off the fixed up value (ARV or After Repairs Value). A rule of thumb for investors is 70% of ARV less repairs. So, for a house that's worth $100K once its fixed up, but that needs $15K in repairs is only worth, at most, $55K to an investor. You might be willing to pay $75K.
If you go after an FHA REO (not Fannie Mae), you have the advantage that FHA has a "owner occupant bid period". For the first 10 days or so after FHA lists a house, only owner occupants can bid. That head start gives you a big lead over investors.
REOs, whether Fannie Mae or some bank, are heartbreakers. If you're the type who finds your dream house and will just die if you don't get that house, you don't even want to bother with REOs. If you can be satisfied with any one of a number of houses, go for it.
If you want to go this route, get out and look at a LOT of houses. Look at some nice, fixed up, move-in-ready houses so you know what the market is like. Then go look at these REO junkers. Make a lot of offers. Include the phrasing "Earnest money to be provided by certified funds with 48 (or 72) hours of contract acceptance." Set a relatively short acceptance deadline, like 48-72 hours. Few banks will respond that quickly, so your offers will be dead before they respond in most cases. They may still respond, though, and now you have to chance to say yes or no.
In general, lowball offers don't work, in my experience. The bank has the house priced near what they want. If you get them down 10% from their listing price you'll be doing good. You're unlikely to buy a house listed at $200K for $150K. The exception would be if its been on the market for a year. Most banks will drop the price every 30 days. That's a good time to resubmit your offer.
Don't get discouraged. You will get a lot of rejections and a few counters. Houses will go under contact to someone else. But those contracts sometimes fall apart and you get a second chance.
The only way I know to get a low down loan is FHA. FHA is unlikely to approve a REO, since it won't meet their standards. So, I think you're going to be stuck with a conventional loan. Even that may be a challenge for some REOs. Discuss this with your lender ahead of time and get an idea of what they will and won't approve, and how much down payment you'll need.
You may be able to get the selling bank to contribute 3% of the price toward your closing costs.
Most REOs are nasty. A good one would only have filthy carpets and dirty walls. New floors and paint inside and out should be assumed. They go downhill from there. I've looked at some that looked like there was a swimming pool in the basement and others that were missing outside walls. One was grafitti'ed on the inside and another looked decent downstairs but had fire damage upstairs. These houses aren't going to be move in ready.
If you want to buy one of these, and get one under contract by 4/30, you need to be making at least half a dozen offers each week. If you find 20 houses you could live with in the next two weeks and make offers on all of them, you just might get one under contact. If you do get multiple accepted offers, use the inspections to look carefully and keep the one you like the best.
You do not have to provide an actual earnest money check with each offer. Sometimes, the seller want's a copy of a personal check. But you hold onto the actual check. If you do get an acceptance, you'll need to get a certified check over to the listing agent quickly.