No problemo!
My GTI was the first car that I bought privately. I was also a little unsure of spending all of my hard earned privately!
But Mkv GTI's seem to be fairly robust overall! Just do all the usual things when purchasing any car, privately or not. Alot of the ones I had looked at were on the long life service plan (serviced every 18k miles approx), but the one I bought had been serviced every 9 to 10k using the longlife oil. But generally just make sure it has a full service history and that the cam belt has been changed if there is more than 40k on it. Or negotiate that into the price (as I did).
If you have the money, definitely stretch for the ED30! I didn't but the standard GTI is still fantastic!