So ten years ago you would have been able to buy yourself a decent used supercar for $50-80k. Unfortunately we are now in a bit of a price-bubble, and prices for used Ferraris, Lamborghinis etc. are way up. Your budget might just get you a high-mileage 360 or a broken 355, but won't really get you the kind of car you probably want.

The market is softening at the moment so prices might fall, but the days of decent Ferraris for less than $50k is probably over.

A compromise could be a Maserati? I know Reddit doesn't rate them, but I think Reddit is wrong and they're great cars. They've not held their value as well so for $50k you have lots of choice: a perfect 4200 or Spyder, an excellent GS, or a cheap GT. All of them feel quite special and sound exotic. Running costs will be high. I would budget $5-10k a year for maintenance. You should also expect single-digit mpg and new tyres pretty much every year.