The standard wheels are 4x98PCD with a 58.1mm bore.
If they're 13" then the chances are they are either 4.0" or 4.5" wide with an offset of 41mm or 45mm respectively. If you have 14" wheels, they'll be 5" wide with an offset of 40mm.
If you look for some numbers that say something like "4J ET41", stamped inside the wheel, then that's what those numbers mean.
The 13" wheel will take something like a 175/70 SR 13 tyre - which has a radius of about 288mm (6.5" wheel radius plus a tyre wall 122.5mm high) so you can fit just about any tyre that is within 5% of that. e.g. 195/45x16 or 205/40x17.
The 195/45x16 likes a 6.5" wide wheel which ought to have an offset of about ET37. They can fit onto a 7.0" but the tyre looks "stretched" if you mount it onto a 7.5" rim.
If your wheel has a bigger offset than that, then it'll be closer to the suspension strut by the difference... and don't forget the tyre is wider too, so it'll likely foul on the suspension. You might need to add a spacer to keep it all from touching.. which is not ideal. Don't go mad with too much offset.
The 205/40x17 tyre likes a 7" wide wheel, again of around ET35. You can fit a 205/40 tyre onto a 6.5" rim but it looks more "bulky" - like you have a puncture...
First work out what wheels you can actually find that will fit your car (4x98PCD with a 58.1mm bore) and then see what each size tyre costs (16" tend to be more expensive than 17") and how easy to find they are (e.g. a 215/35x17, if you wanted wider than 205/40) is more limited and more expensive (i.e. twice the price) of a 205/40x17.
If you can't find a Fiat wheel to fit, you can go for wheels with 4x100PCD and a bore size bigger than 58.1mm.. but you will need special "wobble" bolts and spigot rings to sleeve the bore down to 58.1. The cost adds up... but if you just happened be given a load, they're not any extra hassle to use, day to day.
Don't go mad with a super-wide tyre. Regatta is quite a skinny car, so you'll look a bit jackass if the wheels/tyres poke out of the bodywork too much. As well as it will reduce your economy and be more tricky to steer (old boys' stuff.. but you'll notice it once the novelty of huge tyres has worn off).
Ralf S.