10k will buy you a mk6 gti, straight away I'd be looking to buy private as you save a bit off any garages.
But it will come with a decent amount of miles on the clock, in an ideal world you'd be looking for one with 1 owner from new, servicing I wouldn't worry if it isn't main dealer, as long as it has been serviced well, look for lots of receipts and stuff.
Personally I wouldn't touch a GTI thats had oil changes over 10k just shows it hasn't been cared for, same with tyres, always a good indication of how much money the owner was willing to spend on the car.
Chain tensioner can happen to anyone, me or you, it's just a lottery... work can be done to prevent it happening, changing the tensioner and chain etc, but thats very very expensive and I've heard of 500-1000 being charged for this. I hear not to put the car in gear when parking as any load can move the chain and let the tensioner skip as the tensioner gets it tension from oil pressure, how true this is? I dont know but it makes sense.