Hi SecondHeartbeat. I haven't had a mk6 GTI (I did own a mk6 GTD) and I've been a member on the forum for some time so hopefully can give you some general pointers of what to look out for.
If your budget is £11k maximum, depending on condition and mileage, that would probably currently buy you a late 2009 to late 2010 GTI. With a mk6 GTI of that age, I'd say one of the most important things to be aware of is the timing chain tensioner issue; the tensioner on the 2.0 EA888 series engine in the mk6 Golf GTI is prone to failure and a 2009 - 2010 GTI would have been built with the original version of the tensioner fitted. If it does fail, then you're looking at potentially very expensive repairs. The tensioner was revised 2 or 3 times during the life of the mk6 Golf, so always check to see if the original tensioner has been replaced with the latest version; ask for evidence of this (invoices/receipts for work done) and if it hasn't been done, I'd suggest budgeting for getting it changed a.s.a.p. and use this as a negotiating point with the seller. There's a very useful 'sticky' at the top of this section of the forum (Timing Chain tensioner Failure List) that's worth reading.
I'd always favour a car in good condition with a comprehensive service history over one with a high spec in poor condition as most of the more desirable options can be retro-fitted. Also bear in mind that some GTI's that are approaching 8-9 years old may have been modified by previous owners, and depending on what the modifications are, can result in increased wear and strain on the engine and drivetrain. Other things to look out for or worth considering;
- DSG gearbox; these need servicing every 40k, so ensure this has been done.
- Diamond cut alloys; The 17" standard wheels on the GTI were powder coated, but many GTI's came with the optional diamond cut 18" Monday Shadow wheels. These are prone to white worm corrosion and a good diamond cut refurb will cost in the region of £80-90 +VAT per wheel.
- Tyres; the rear tyres can wear excessively in a 'stepped', 'sawtooth' pattern on the inside edge (you can see and feel this). If they have, they'll be quite noisy and make a noise that's characteristic of worn wheel bearings.
- Xenon headlamps; not many GTI's have these, as they were an expensive factory fit option. I had them on my GTD and they were very good, so a bonus if you find a car with these fitted. The ED35 had them as standard, but this model will be outside your budget.
- Leather trim; this was an option - standard upholstery is red "Jackara" tartan. VW leather isn't the best quality and is prone to sagging and creasing, especially the right hand bolster on the driver's seat cushion. With the cloth seats, check the bolsters for excessive wear, especially the drivers seat right hand backrest bolster.
- Radio/CD player, standard fit was the RCD310. On the early mk6's this was backlit in blue which looks a little odd when the rest of the switch gear has red backlighting and the instrumentation is backlit in white. Optional units were the RCD510 (6 CD player, with touchscreen) or RNS510 (as RCD510 but with sat nav). RCD510 / RNS510 can be easily retro-fitted.
- Bluetooth; was an option. If not fitted, this can be retro-fitted.
- LED tail lights; unless retro-fitted, a 2009-2010 GTI won't have these, but were a popular retro-fit by owners.
Good luck with your search. I hope you find the right car!