There's nothing inherently wrong with a car like you describe. In fact I think if you looked at things historically Porsche is building more reliable cars now than ever.
Having said that, there is no way that a $20,000 used Boxster is as safe a bet as, say, a used $20,000 Lexus. The reason I say that is that if you do run into problems they can be very expensive. A $400 clutch is a $1,200 clutch in a Boxster (or something like that).
You can purchase an extended warranty, and this would probably be a good idea. The way I look at it, though, is that you can basically steal a $50,000 car with a couple of paint chips and wear on the driver's side floor mat for $20K! Resale values are just way, way down.
Mod the car to get it to be responsive? And you've been driving an SUV? Hahaha I envy the feeling you'll get on your first test drive!