All recent Fiats have wheels with a 4-stud, 98 PCD stud fitment (or 4x98 for short).
98PCD (Pitch Circle Diameter) is the diameter of the imaginary circle you would get if you drew a circle that passed through the centre of all the stud holes.
( You can fit wheels with 100PCD .. but you need a special kind of bolt that takes up the difference - a wobble bolt. 100PCD is obviously a 2mm bigger diameter circle than 98PCD so each hole is 1mm further out than needed. The wobble bolt has a loose seat, so the seat lines up with the wheel hole, while the stem lines up with the hub )
Anyway.. you also need wheels with the correct centre bore. Fiat uses a centre bore of 58.1mm Wheels generally come with a larger bore and you sleeve the bore down to fit whatever car you have with a spigot ring.
Spigot ring fills the space between the inside of the wheel bore and the axle stub on the hub. It's job is to make sure the wheel sits snugly on the axle stub, so that the weight of the car rests on the stub. If you leave the spigot ring out, the wheel isn't being held up except by the pressure of the bolts when you do them up. It's a bit risky, shall we say?
After you have 4x98 and spigots sorted out, you need to check the offset. This is the distance between the centre of the wheel and the hub face, in millimeters. The value is shown as ETxx where xx is the distance/offset.
Punto uses an offset of around 40mm (look on your wheels - it'll be stamped on there) so you want 4x98 wheels with a 58.1 mm bore and ET40 (or whatever).
Obviously PCD and bore size are crucial but don't get hung up on offset.
ET40 sticks "in" more than ET35.. so if your new wheels are ET35 then they're 5mm more sticky out than the old ones. It's not much.
Don't forget that your alloys will probably have bigger tyres on, which will increase the width of the wheel/tyre. Don't go for a much too different offset or the tyre may rub on the suspension or wheel arch. A few mm is fine.. have a look in the arches and see how much room you have.
Don't forget the wheel has to be able to turn (front) and suspension compression will also affect if it's going to touch anywhere or not.
Finally... just when you thought you understood it

you havce to fit the right tyre.
The size of the tyre denotes how "big" it is. I'd guess you have something like a 165/65x14 on it. That's a 14 inch diameter (inside bead), 165mm wide with an aspect ratio (the height of the tyre) that is 65% of the width. (65% of 165mm in this case = 107.2mm).
The new tyre must be the same as this figure, so that the rolling radius is the same. This determines if it will fit in the arch

and it keeps your speedo' accurate.
A 14" wheel has a radius of 178.8mm. If you add the tyre height of 107.2mm you get a combined wheel/tyre radius of 285mm. The new wheel/tyre you fit must be the same size.
For 15" wheel, the wheel radius comes out at 190.5mm so to get a wheel/tyre size of 285, the tyre wall height has to be around 95mm (190 + 95 = 285)
If you fit a 195/50 tyre, the tyre height is 50% of 195 = 97.5mm (or 2.5mm bigger tyre than that 14"). That's close enough.
For 17" you have a wheel radius of 216mm, so the tyre wall height has to be 69mm. A 205/40 comes in at 82mm so you have a combined 298mm radius (13mm bigger than standard) which at 4.5% bigger I'd say is too much.. but it will fit.
Consider a 16" rim (less fashionable, but...) You get a 203mm wheel radius so you're looking for a 82mm tyre wall height. a 195/45 at 88mm gives you 291mm combined radius... just 6mm more than standard.
A bigger aspect ratio gives you a higher sidewall (relative to the width). As you can see above a 195/45 has a sidewall 6mm taller than a 205/40 (88mm vs 82mm respectively) so you get better ride comfort. A taller sidewall acts to cushion road shocks... but a 40% ratio does look better.
Ralf S.