"Cheap" is a relative term but if you're looking for the least expensive rooms, those would be at the Value Resorts (ASMo, ASMu, ASSp, POP and AoA). However, they are also the most remote when it comes to park access. That means that you will spend more time on Disney transportation than if you were staying at a resort that is on the monorail or within walking distance of Epcot. If your son has mobility issues and uses a wheelchair or
ECV, that could make your wait for transportation even longer, given that buses can only accommodate a few of those assistance devices at one time.
If you want to be able to squeeze as much out of your $100/person that you will pay for single-day tickets, I recommend that you go for broke and spend more for your resort room. Get the best possible discount that you can find for a monorail or Epcot resort and stay there for your one night. CR Garden Wing rooms are the biggest bargain for your Deluxe dollar. Renting DVC points for a studio at BLT, VGF, BCV or BWV can also be an affordable way to stay deluxe for one night.
I would also choose whichever park has the latest hours your visit. It would really bite to pay for a day at MK only to learn that there's an early closing due to a hard-ticket party or private event.
Arrive at the park as early as possible and plan to leave at closing if your family can tolerate it. Choose counter service meals instead of table service. You'll save time and money. You'll get plenty of table service dining on your cruise.
Go with a "plan of attack" so that you can get as much in as possible. Visit the touring plans websites to learn which attractions are being rehabbed so that you don't end up trekking over to BTMRR (or whatever attraction you want) only to learn that it's down.
Download the My Disney Experience app to your smartphone so that you can check wait times and FP return times (if Disney is still using the old FP system when you go).
Learn about Magic Bands and FP+. If your resort participates, you will be able to choose 3 Fastpasses in advance as long as you have tickets linked to your reservation.
Read up about the changes to GACs (replaced by a program called
DAS) which went into effect earlier this month. It will make your visit go smoother if you know what kind of accommodations to expect for your son's disability. Being informed now will save you time later.