At my own house (where I've lived for 25 years), I have a well, pump & septic system. The county requires an inspection of the septic tank/field whenever the property changes hands (which means you pay for a contractor to pump it out, clean it, check for cracks, etc. - about $400 here), but the pump, supply lines & pressure tank are all up to you. It's also required to have a percolation test (septic) & a water-quality test (well). The things that usually go wrong are:
1. The septic needs pumping out - people put stuff in there that they should not. VERY common.
2. The pump dies. Find out how old it is, if you can - 25 years is an expected life-span.
3. The pressure tank bladder starts to lose air & although it can be re-charged, it will eventually need to be replaced. Again, find out how old it is - 10 years is a good time to replace it.
4. The well goes dry. No solution for that!
5. It's possible for the leach field to clog up - has to be dug up, pipes replaced & re-installed. $$
All that being said, if the water is certified potable, the septic tank & field are functioning (get the tank pumped, anyway) & all pipes, switches, tanks, etc. look in good order, you're good to go.
You may get some push-back from people who aren't familiar with using a well/septic system, but if you can provide proof that you've done everything to check for safety & functionality, that will go along way toward selling your property. Good luck!