I would say you're on about your limit to get much of either for £1000. The punto depriciates a lot more than the corsa (as with all fiats) and hence is probably your best bet. Bushboy is correct, too many Corsa's. I don't have a huge alligiance to the Fiat brand, just drive one because they are cheap. DOn't expect more than mediocre build quality from Punto but you can't expect more from the bottom of the range Vauxhall either.
Thing to watch on the punto, make sure it has the RED KEY when you buy it. It holds all the info for the immobiliser and ECU, without which you might have problems in the future. Total cost to fix is about £600-800 from a Fiat dealer. It annoys the heck out of Fiat Punto buyers supposedly.
The Citroen AX isn't a bad bet or the Uno at the lower end of the market (N reg topping £600 down to K-reg worth no more than £300) Compare that to the Punto or Corsa...!
WIth regards to your theory and driving test, best of luck. Get the "Focus - passing your theory test" CD, about £10 from Smiths, very good and has hazard preception practice too. Worth it if you only have to take your test once because then it is done easily! Depends where you are in the country but again, Bushboy is correct, most places have waiting lists around 8 weeks so you would be lucky getting it so soon. For me, I was lucky, was going to have to wait about 8 weeks but got a cancellation very quickly on friday 13th.. No guesses to why I got a cancellation on that day!
SO to summarise, I wouldn't agree the Corsa is crap, especially not relative to the Punto, if i were you I would see what your money would get you and try both to see which you prefer - it comes down to a personal preference at that point.
Rgds and hope I have been of some help.
Paul