Be careful using the DOT 4 fluids. They are not compatible with the seals in the majority of the aircraft brake systems, and will remove paint quite easily. 5606, Aeroshell 4, Aeroshell 41. ROYCO 782 are great choices. Yes, you can use automatic transmission fluid, too.
Whatever you use, do make an entry in the logbook for yourself and future owners
Most of them are comaptible with each other, but no sense mixing if you don't need to.
Avoid SKYDROL.
Vic
As vehicle brake fluids were mentioned here: One of the major differences between any hydraulic oils and DOT brake fluids is, that DOT3 or DOT4 are strongly hygroscopic, i.e. brake fluid is designed to absorb any water which made its way into the braking system - up to a certain amount, of course. This way, it will effectively inhibit internal corrosion inside the braking system. However, the more water the brake fluid absorbed, the lower gets its boiling point. When brakes heat up, the fluid may then (partially) evaporate. Steam or gas won't transfer the hydraulic pressure very well which can cause brake fading. It is therefore essential to regularly drain and replace DOT brake fluids - in road vehicles not later than in 2 years intervals. This may not be the only reason why I haven't seen much DOT brake fluid use in aircraft.
Not sure how internal corrosion prevention will work with hydraulic oils or ATF and which replacement intervals are needed here.