I think I would go for the 2005 gray one.
I currently have a budget thats around 10k.
My current findings are:
20th AE gti for 9500 (65k miles)
2005 black gti for 8250 (90k miles)
2005 gray gti for 9500 (40k miles)
2006 black gti for 10,450 (92k miles)
All are manual transmission.... and yeah.
I don't know which one I should choose.
Also that 20th AE GTI with 65k you will want to see if the timing belt has been changed because that will put you back $600-$800 as they are recommended to change at 70k miles.
Are any of them modded, or had been modded and put back to stock?
The used car market has some great finds, but you need to check them out in person and check maintenance records.