Since you have an ATX, go and buy one of those cheapie pump-up weed spayers. Also buy 4 quarts of ATF and 2 gallons of mineral spirits. Mix the 4 quarts of tranny fluid with the 2 gallons of mineral spirits and put in the sprayer.
Wait until you have the new covers in hand and then place a lot of old newspapers under the car.
Start with the tranny first. Spray at the exposed "guts" from all four sides. Any dust or grit that might have gotten blown in there will be washed out by your spray. Let it drip for a good hour and then put on the new pan and gasket.
On the engine, poke the wand, with the nozzle set to wide spray, into the engine cavity and work from the top down as much as you can. Most of the contamination is going to be very small particles that can be carried by the wind. Don't used compressed air to try and "dust off" the internals, just the weed spayer.
Let the innards drip dry for an hour or two and then with a clean shop rag, wipe clean all the surfaces that will be getting the end seals and the silicone gasket maker, not the inside of the block.
After assembly, fill with tranny fluid, new oil filter, and run at idle for 10-15 minutes, reving it to no more than 1,500 or 2,000 rpms every once in a while to get a wave of oil flowing over the windage tray.
Stop engine and drain oil and put in another new filter.
Don't rev the motor over 2,500 rpms for 5-6 months.
Just kidding on that last one.
Have fun.
Tom