Do not wet sand. Don't put anything remotely even approaching sandpaper on your car. I even remove my Crossfire from the workshop when bead blasting in my sealed, filtered blasting cabinet just so there's no chance of grit getting on the car. If you wet sand, you will run the risk of going through your clearcoat. Once that's done, it's game over for that panel.

Clay bar only. Do NOT use your fingernail. Just use the clay bar and use lots of Clay solution. Never clay dry. Keep rubbing that clay on until that crap comes off. I've clayed off urethane paint overspray on cars. It will take car of those "water spot" stains.

Dispose of old, messed up clay. Use new clay bars. When I buy new clay bars, I cut them in half with a knife and knead them into thin sheets.

It sounds like the previous owner of that car left a lot of crap on it. If it costs you $50 in clay it will be worth it in the end for that perfect finish.

By the way, remove as much loose dirt using water and a mild detergent as you can before claying. Only use clay on the stuff a gentle swipe of cotton microfiber won't remove.

Also, do not wax your car until you've removed every bit of crap from the surface. Otherwise, it will be swirl mark city, I assure you.