Gratz Bro! Ya you did good, especially if you were dealing with a trade in with the mix. As far as the tranny goes, PLENTY of reading here about whats up. The hardest issue is finding a reliable shop. As I have learned stay away from AAMCO and the like, all they want to do is pretend the whole thing is shot, and then either swap one out, or say they did to get max profit. I found a solid guy who took over the business from dad. Tests can be done at the PCM to see if its the solenoid, but that needs a good shop as well. One of my early threads here has a video from a Cali specialist for example. As far as the PCM - DO NOT go with ebay/pre made rebuild. Waste of money and having to deal with programming the new. SIA Electronics is what the guys here use, its listed in a couple threads or can be googled. You just have to pull and ship.
Now I tend to lean to the internals on the tranny. Your car being a rental makes me think there probably was some hard drivers in that time frame. Also, they pretend that this is a 'sealed' tranny and needs no maintenance, but it does. What that means to me is most owners never had a service done on it. You should at least do a full flush and swap on all fluids in the car, including the Tranny. This means the mech would drop the pan, and that can give you better clues whats up. At that point do like I did and replace both the shift kit AND the solenoid if needed. My mech didnt think the solenoid was bad even at the point of doing the work, but he was in there so why waste another labor fee when it would fail. It turned out my control springs 'crumbled in his fingers' even though they looked good during inspection.
Enjoy the new ride!