This is going to come off sounding real negative, and I do apologize. Rescues are not the place to get a first horse, which I know is not what you want to hear. It may evoke a romantic notion, but there's a reason those horses are in rescue situations, and no decent rescue should send one of their horses out to a first time horse owner (which, really, is just my very blunt opinion.)
I always recommend folks take six months (minimum) of lessons from a reputable trainer before buying a horse. This allows the potential owner to get some practical experience and know how, plus will help them make an educated decision when they go out to buy a horse (if they even are still interested, and several aren't.) Even though you've already got the horse, I'd suggest getting lessons on someone else's horse so that you're ready for your own.
There could be any number of reasons your horse is going down, but I'd guess it's because he's figured out it's how to get out of working. This has nothing to do with his breed, but his work ethic and the fact that he's gotten away with it. Still, getting a vet out to check his teeth wouldn't be a bad idea, and having someone show you how to fit a bridle is in order as well.
You could also begin checking out several videos from trainers to get a feel for ways to deal with your horse; Pat Parelli, Ken McNabb, Clinton Anderson or any number of other 'natural' horsemanship trainers will be very useful. I'd watch more than one trainer, as they all have something to offer and no one is the end all answer to horsemanship.
I suspect you're in a bit over your head here, but hopefully you'll be able to find someone in your area that may be able to help you. Check at as many feed stores as possible and head out to some horse shows to get names of farriers, vets and trainers. You may find out that the ones you've got aren't real reputable, or you may find that folks love them. At the very least, you'll have a second name to fall back on should you need someone else. Good luck, and keep us updated on how things are working for you!
(And yes, appaloosas have notoriously bad feet.)