Hi, and sorry to hear about the loss of your father.
I'm assuming you have experience working on cars and a set of basic hand tools/jackstands/etc. If that's not true then the best first step is to take it to a garage and have them do an inspection. Nashville is a big town so I'm sure somebody has NSX knowledge. If nothing else, the Acura dealer will probably have a certified tech who can baseline the car for you.
First, download the factory service manual by clicking on the link in my sig line (below). I'd start out by refreshing the brakes, probably starting with a new master cylinder, and then bleeding them. If you don't get a solid pedal feel after that let us know and we'll troubleshoot further.
Next is to change oil and gasoline fluids and filters. Drain the oil and re-fill, install a new Honda oil filter and crush washer. After that, drain the gas from the tank and change the fuel filter (strainer) that is in the engine bay. Pull the injectors and have them sent away for cleaning as well.
After that I would start working on the cooling system. This is really critical because the process is very different for the NSX vs. other cars, and because these engines are aluminum an overheat can quickly blow a head gasket and warp the head. Rather than spell out the process, take a look at the wiki here:
http://www.nsxprime.com/wiki/Coolant_Flush_and_Fill
One more note on the cooling system. You're going to want to replace all of the coolant hoses (about 20 of them) because they degrade over time. I wouldn't drive the car very far, and would keep a laser focus on the temp gage until this is complete.
If the car is still running rough pull the rear bank of coils (it's a coil-over-plug setup) and look for water marks or burning. Water gets into that area and the coils go bad. If that's the case then you'll have to replace them.
Assuming you've done all of that, you now have a car that runs, stops, and probably won't overheat. There is a lot more to do for preventative maintenance (you're going to want to tackle the timing belt, get the valves adjusted, etc.), but hopefully this lets you get a baseline on the car.
Last thing-these cars are going up in value and this one has a personal connection. Don't let somebody scare you into selling it by showing you a big repair bill. Yes, they can get expensive but they are DIY friendly and this is a good community. Good luck!