My opinion (heart over head): early-80s Bertone VS model or X1/9 IN. With red leather interior, two-tone paint (silver over black) and the colour split line tucking up over the wheelarches, like this:
I think most would agree that the above spec. and colour choice is the most elegant and quintessentially 'X' X1/9. Grown-up, refined, and sharp: trimmed nicely, and just somehow looks 'right' for an early-80s car.
Practical advice: any year without rust. Preferably post-'80 with fuel injection for 75bhp with reliability.
Reasoned opinion: early model (pre-'77) with simple interior preferred by the purists and smaller bumpers (though in my view, no less ugly than the big ones, they stick out at awkward angles!) Usually in lurid colours and clearly a 70's car.
You mention that you're happy to restore it, but be aware that restoring an X1/9 can be $$$$ and difficult since the panels are scarcely available and rust attacks the structure in very inopportune places. Since you're in the US I won't bother with details of euro-only FIATs
but suffice it to say that 80's FIATs with bolt-on panels resist rust much better than X1/9s of any age, the X1/9 is basically a 70's car. It needs to be well-kept.
I have heard that early Bertone models (such as the one pictured) suffer from worse rust than earlier or later models.
I think that you already have my opinion plus much of the above info from the XWeb discussion forum, ah well
-Alex