Buy, for sure. It’s almost always cheaper and you won’t be stuck with another car you don’t like. New or used is harder. With your limited means I’d say used, but not more than about three years, and it must have full maintenance records. If you plan on keeping the car forever, buy new. If you have the car for a decade or more, the difference in cost between new and used becomes insignificant, and with a new car you’ll know exactly what you’ve bought.
Of the cars you name, I’d stay away from the Fiat. It’s cute, but ultimate reliability is still unknown and it’s overpriced for a low-powered, modestly-equipped car. If you want small and cute you’re better off with a Mazda2. The Hyundai Accent and Kia Rio are also good bargain choices. They are all modestly equipped (like the Fiat), efficient, well made, roomy in the front seat, light and airy, and just nice. Hard to describe why, but they feel sensible, not cheap. The Yaris is also OK, but somehow doesn’t feel as nice to me as the others. More of a sensible shoes car. Also in that category is the related Scion xD, with a worse interior than the Yaris.
In the to-be-avoided group I’d put the Chevy Spark (tiny, tinny, slow), Chevy Sonic (reliability problems), Ford Fiesta (some reliability issues, overpriced, cramped, but cute), Scion IQ (unless you like clown cars or have no legs), Smart (slow, not as efficient as it should be, terrible at speed), Prius C (a Prius in name only, cramped, drives poorly, and not as economical as it should be), Nissan Versa (Consumer Reports and auto magazines agree on this - they hate it - and so do I), and Dodge Dart (questionable reliability, interior out of a 1990 Pontiac). I probably missed a few. Some of those are not terrible (and some are), but they all have some disadvantage I can’t overlook when there are better cars around.
The Fit is a hair pricier than those cars, but it’s also roomier (massively) and a little nicer. Everyone loves the Fit. Auto magazines think it’s fun to drive (if not quick), and Consumer Reports says its reliability is excellent. I might have bought one a year ago except most of our driving is long distances on freeways and the Fit isn’t the most comfortable car for that. We wanted something with a few more amenities. If you mostly commute or drive around the city, the Fit is ideal.
In the stylish, fun, but slightly more expensive category I like the Hyundai Veloster. It’s surprisingly roomy for something that looks so tiny, and it has loads of personality.
I like both the Prius and the Golf, too, but think they aren’t a good match for your circumstances, being quite a bit more expensive. You sound as if you should be budgeting for an economy car, and those are a big step up. The Golf has OK reliability, better than most German cars, but it will still likely cost more to maintain and repair over its life than one of the better economy cars. The Prius is a nice car and very reliable, but it costs more up front and you won’t get that repaid in improved economy for a few years. A much cheaper car like the Fit will cost you less overall unless you do massive amounts of start-and-stop driving, where nothing beats the Prius.