I have a 1967 1.2 Fulvia Coupe that I use as a daily driver. It is far from perfect, but I just love everything about it. I have put 10,000 miles on it since getting it less than a year ago.
Parts are now very available through lalancia.com, Adan who runs it is just awesome to deal with.
Ed L will give more input into specific things to look out for, but for me it's good brakes, solid engine with no obvious issues and overall complete car with no critical rust issues. (mine still has lots of rust but nothing I can't live with at the moment).
Mine's a 1.2 and I do wish it was a 1.3, but I'll bore it out once the engine craps out.
Gets a little warm in the car on super hot days but 90% of the time here in Southern CA that is not a big problem.
email me direct seth at carmichaelfilms dot com I'd love to see what you are finding.
1960 Lancia Flaminia PF Coupe 2.5, 1967 Fiat Moretti Sportiva, 1967 OSI 20m TS, 1967 Lancia Fulvia Coupe 1.2, 1968 Lancia Flavia 1.8i