Unless carbon fiber manufacturing methods change for the better (as in cheaper), the fact that it's carbon fiber automatically knocks it out of entry-level positioning.
The Alfa 4C is the cheapest carbon fiber car currently available and that's North of $60k.
Aluminum seems to be headed toward "everyday" status as a car material, however, so maybe if it were made from aluminum that could be a nice middle-ground between weight savings and production cost.
As far as the top goes, how about a hybrid between a targa and a convertible? Let the targa part be similar to the X in that it is a lightweight panel that is manually removed and stored forward; the convertible part would be similar to today's folding hardtops, in that only the targa bar/rear sail & window folds or drops away out of sight. That way you could have three modes: full top up, targa top off, or full topless mode.
As far as engine goes, I'd want a better engine than the 1.4 turbo. Maybe something like a slightly detuned version of the 1.7 in the 4C that still lets the 4C have more performance to maintain the brand hierarchy.