Wah! Its all moved about!
Neily .....Yep, it`s in the right place now
Anyway, the tyres on there are 175, so a switch to some form of alloy wheel possible wouldn't increase the tyre size, well, I wouldn't want it to, its pretty much that thats governing what type of wheel I would put on it (that and it has to suit the car obviously).
As for different tyre sizes altering grip levels...its an odd on. Excesssively (sp) wide wheels/tyres will reduce grip in most environments simple because they reduce the pressure on the road surface (pressure = force/area etc..etc..). The only time hugely wide tyres would be an advantage would be in extreme conditions i.e under heavy brakeing, heavy acceleration or anything which would increase the force on tyre above and beyond 'normal' conditions. From how this Chevette feels on the road, I think the 175 tyre width is about as wide as I'd want to go.
All that aside, possible the most important thing about tyres is the quality, slap a set of £20 'Ditch Finder Pros' on and you'll be sideways into a ditch before you know whats happend!

Thankfully that one came with almost new 'Kumhos' on each corner, not the best brand but I've had them on other cars and they've performed fairly well!
While I think of it, I also got a set of what look like rim covers, crome things which clip to the outter of the wheel, I can only assume these are designed to go on the rostyles rather than the standard steelies?