If you can't afford good year/Michelin/conti's etc then go mid range like vreds or something rather than go budget ditch finders
+1
Problems with cheap tyres (in my own experience on older / cheaper cars, plus the rubbish fitted to my GTI when I bought it):
Noisy
Poor braking grip (esp in wet)
Poor lateral grip
Poor traction
Badly made, requiring lots of wheel weights
Harsh ride
A GTI is a very frustrating car to own on a budget - too thirsty, for a start. Seriously, I'd rather have a budget car on good tyres than the other way round. I love my GTI, but in your shoes, I'd sell it and come back to the party when funds allow.