I've sold my last 3 cars privately - Clio F1, S2000 & Clio Cup.
I had no problems with selling them, test drives, tyre kickers or payment process.
The only problem I had was time to sell the car, cost of advertising and keeping it continuously clean etc.
All my cars have been pretty rare in the whole scheme of things, so not on everyone's wish list (ie not German
). Therefore if you get 3+ interested buyers then you should sell the car.
I have always made sure my car has HPI Certificate, RAC Mechanical inspection and in excellent condition. If you are honest then it will completely obvious to potential punters.
Take £150 deposit, with 95% value of sale price as a bankers draft or cleared electronic transfer, then they can bring along 5% in cash for negotiation - which hopefully you will keep
I hope this helps but I have not sold an Alfa privately and I think most punters might be hesitant - so even more reason to have everything in place