I would do a search for AOD on this forum and spend a couple hours of reading. There's all kinds of different ways to go from "cheap, but will work" to "expensive, but you can't break it".
The AOD, it seems was in a constant state of change from it's inception in '84, constantly getting better. They say that the '84's are the fragile ones, but that's what I have in mine and haven't been able to break it.
There's also the issue the goofy shift pattern. Many people don't like it, so opt for after market valve bodies. Since there is only 3 forward drive positions on the shifter, but 4 forward gears, things get a little bizarre.
On a stock AOD the shift pattern is like this:
3-automatic shifts from 1st, 2nd, 3rd, OD
2-automatic shifts from 1st, 2nd, 3rd ... OD is locked out
1-Holds 1st or 2nd gear depending on which you're in ... will also downshift from 3rd/OD to 2nd gear if RPMs are low enough to not explode the tranny.
When drag racing a stock AOD, shifting is really wierd, but you get used to it pretty quick. It's just like manually shifting a '65/'66 GreenDot C4.
If you're on a budget, I'd recommend finding a low mileage AOD from a PicNPull, putting in a decent converter and shift kit. If money's no object, Lentech makes a very nice, stout AOD.
For the conversion stuff, check out Windsor Fox.
I used the WF shift linkage and x-member, the Lokar TV cable (a TV cable/rod is a MUST) and had a stock AOD flexplate machined down to correct imbalance when my engine was balanced (it was way cheaper that way).
Good luck ... it can be a pain getting all the parts and getting them working right together, but is well worth the effort!