Congrats on the new car mate, haven't seen many white ones, looks like a tidy example.
How could you possibly think a 1800 integra would keep up with a 3ltr TT Supra?
Your spoiler does look like a universal item, Whats been done with the original spoiler holes,? have they been filled or has it just got plastic gromits in the boot where the bolts used to be?
If its got gromits, get the original spoiler back on there mate, or even better, get one of the TRD replica ones
http://www.whifbitz.co.uk/images/parts/bodykits/suprarearspoiler.jpg
Good luck with the new car, and the best advice I can give you, is take it easy, these cars bite when provoked, epecially in the wet.
I think a Jeremy Clarkson statement fits the supra quite well, "its like owning a bear, its all well and good, until one day, it bites your head off".