Main issues with the 20vt are:
Cambelt and ancillary belts - These should be replaced 45-50k or 5 years depending on the mileage/age. Fiat charge ££££'s, but other specialists will charge around the £400-£500 mark for the same work.
General wear & tear components:
Exhaust tends to fail on the OE system, and the tailpipe can fall off, which will lead to a melted rear bumper, new exhausts are from £170-£300 depending on what you're after.
Wishbones can fail quite early, (allow anything from 30-60k), there not that expensive but are a bugger to fit DIY.
Manifolds can crack early too, you'll hear a tick from the front of the engine, or blowing if the crack is loud enough. You'll also notice a fumey smell from the front too. Particularly evident on cold start up, as once the manifold is warm the crack can close up, and be less noticeable. Allow up to £500 for a new manifold and fittment.
Other than those listed above, just look out for the usual general stuff which wears out.
Smoke from the exhaust is generally not a good sign.
Bouncing along an uneven road is a sign the shocks are worn.
Etc,Etc,
Issues which are fine:
Squeeking front brakes - this is usually not a problem, just indicative that the car has had pattern, or aftermarket pads fitted.
Small squeeks and rattles from the interior - they all do this to some degree, and again not really an issue.
Good luck!