To the OP, or anyone else that has not been to an FSAE race or have been part of a team. .
Working out all the problems is going to be hard. And making it reliable enough to race consistently will be even more time consuming. And if you find a monocoque car . . good luck. Even very well made cars are going to have difficult problems. Teams wrestle for weeks to fix little glitches (but still, they are students!) And often times even the well placing schools' cars don't work as well after they have finished the race! However, a couple of schools come to mind. They have great history in doing well at FSAE, and take their cars out to full sized car circuits and run laps. Those cars are VERY reliable in FSAE standards.
But if you are asking that question I guess you have enough fabrication knowledge to upkeep the vehicle.
nd a word of warning is that not all FSAE cars are created equal. Some cars are very nice and quick, some cars are very well put-together and professionally made but very slow, other cars are just plain junk. Some schools have been capable of building one that works fairly okay in a few months order. Other schools, as a result of the worst groupthink and badly fragmented teams, build horrible cars even with adequate resources and time.
I think the real value in used FSAE cars is really the sentimental value the alumni have.