Bench preparation for new transaxle.
Thankfully yours is clean, otherwise clean it thoroughly with brake parts cleaner and WD-40. Why brake parts cleaner? Because it dissolves grease and oil nicely, plus evaporates away. Wear gloves and do it in a well ventilated area or you'll see visions of Jimi Hendrix.
As mentioned previously, that transaxle looks like it was washed off with a pressure washer so you're going to have to flush the transaxle somehow. First try to drain out any water that may be in it. Then just pour oil into the transmission through the fill port and let it drain out of the drain port. It'll probably never be perfectly clear as it's always going to pick up some old oil from inside the transmission, the main thing is to get the water out.
Couple of points to consider in order to get the new transaxle ready to swap in. Taking care of them now will save you headaches down the road.
1. Once you flush it you'll have to transfer over the fill tube and reservoir from the old transaxle. Be careful installing the fill tube as the fill nipple is plastic and only held on by one screw. I've had problems before with the fill tubes that have the spring stiffener in them actually pulling the fill nipple away from the body of the transaxle and causing it to leak.
2. As stated in my last post the auxiliary hydraulic line fittings are flare fittings and they're sealed to the transaxle with o-rings. Two o-rings per fitting to be exact as it has to pass through the transaxle case first before being attached to the pump inside. Any damaged o-ring or dirt in there will cause you fits with a leak. Thankfully the fittings thread into the pump and then are tightened to the case with a lock nut to keep them from moving. Make sure the previous owner didn't loosen these fittings or the locknuts during disassembly. If so use a generous slathering of pipe dope over the fitting as it passes through the case. Mine leaked constantly until I used pipe dope and I haven't had a problem since, just try to keep it on the case and not inside it.
3. The top seal can cause you fits if the transaxle was overheated. It's not hard, nor expensive to replace, but it will throw oil all over the transaxle and make it a pain to trace down where any potential leak is coming from. Thankfully Tuff Torq no longer sells this seal, but it's a somewhat common size, so you can get them anywhere for cheap. I forget exactly which size it is, but the JD guys know as they have problems with theirs leaking all the time. Otherwise you can read the Tuff Torq parts manual to find the seal dimensions and order off that, I think that's what I did. If your transaxle looks like it was overheated at some point (evidence of oil leaks or lots of buildup on the fins) then replace the seal now. Otherwise you can replace it once it's in the tractor, but requires removal of the seat pan.
4. Replace the inner filter if you have a new one. Be careful as they're expensive. If you don't have one I probably wouldn't worry too much about it unless the transaxle has a lot of hours on it, but as you said yours shouldn't.
Installation of the transaxle is the reverse of removal. I would take the time now, however, to clean up the tractor before putting the transaxle in, but that's just me.
When you go to fill the transaxle just take your time. I can usually get about 3 quarts into it quickly, it's the last quart that takes the most time. Don't use a funnel as it'll just make a mess when it overfills. As said before, leave the seat pan off so you have full access to the fill reservoir and fill it to the brim each time. Be careful though, cause if you overfill the transmission you'll have to drain some out. One of those suction drainers work great for that.
Don't worry about filling the differential area separately, oil will get in there from the case. Just don't leave that fitting open as it'll leak out of there when you're getting close to full.
As far as cleaning out the auxiliary lines, you can try flushing them out with compressed air, but there's a lot of bends, twists, ports, and fittings to go through. Basically a lot of places for shavings to get caught up.