As much of a spoil sport as Rakey sounds, he is very right.
Remaps and chips are detectable, don't be fooled. Even those that can be reversed don't use the original MINI map when they are reverted to "stock". As I said in my earlier post many of the maps/chips available don't boost the Cooper much anyway, so is it worth the risk of having an undeclared one.
As for alloys and bodykits, insurers have mixed views on these. When I tried to declare my Aero kit to MINI insurance the premium went up £300, and I'm 32. My current insurer isn't bothered about it at all, but then I have all my many performance mods declared, and the bodykit is only minor. Think you'll find your £1900 rises rapidly when you start modding, even on your parents insurance. You'd be best buying a car with the 16/17" OEM wheels than going aftermarket. Just choose your car carefully so it's as close to how you want it without the mods.