Rolls forward in neutral, locks up rolling backwards??

Stop right there. You don't realize that 90% of a tf's problems arise in the two front drums that you are already familiar with. The front drum that has the tabs on it that lock into the slots in the sun gear shell is the drum that holds the clutch pack for third gear; and it is also used in reverse. That front band is the only thing stopping it from dropping right out. It's easy to check the condition of the clutches; even if you don't want to replace the piston seals inside of it...The only other thing I'm suggesting is checking the clutches in the "forward" drum; which is the next one in there; the one that has the input shaft sticking out front. It's called the forward clutch because it's engaged when you put it in Drive, and stays engaged for all forward gears. Leave everything else alone and you won't get in over your head like so many first timers do.
Thanks CudaFact, that's actually exactly what I wanted to hear. I feel comfortable pulling the drums and inspecting/changing the clutch plates and steels, but I'm sure we all know how easy it is to follow a rabbit hole and suddenly realize you've got the whole car apart and have no idea what you're doing or how you got there.