My GTA has almost 160 thousand miles on the clock, I would be checking:
1. Rust - These are old cars now - Check the floorpan, wings, sills and inner arches as all these are known to rust, in some cases badly. Check the rest of the bodywork and general condition of the paint, front wings are known to rust and are now out of production
2. Engine - Check the header tank and under the oil cap, you don't want to see any oil in the coolant header tank or mayo under the cap as it could indicate head gasket issues. A compression test is the best way to confirm. It's a few grand to rebuild an engine
3. Timing belt - Opinions do vary, but I would change mine every 3 years (or 40k) along with the tensioners and idlers, also, change the water pump every other timing belt change
4. Suspension - The shocks, especially rear ones, do collapse. Also check the rest of the suspension arms. A full-on suspension overhaul is easily £2000 (roll bars, shocks, springs, arms and wishbones that is)
5. Clutch / Gearbox - The clutch should feel quite light, check if it bites high which might indicate a worn clutch (replacement clutch £550-£600. Most cars should have a limited slip diff, either a Q2 or Quaife, if it doesn't it is worth fitting one as the GTAs are no stranger to blowing a standard diff. Clutch replacement and fitting of a Quaife diff is around a grand. Gearboxes are rare and some of the parts are now out of production, make sure all gears engage smoothly.
6. Oil Cooler - The cooler pipes corrode at the unions, there is a kit available but it's worth checking beforehand
7. Silly things - Wheel arch liners, front ones can be in a bit of a state and are now out of production. Engine ECUs are out of production (Autolusso can supply a replacement kit for £2k). Does it have xenon lights? Parts are rare and expensive to replace so make sure they work and align properly
As a short story, I bought my GTA for £4500 with 150k on the clock, almost three years later it owes me about £12k all in but it's a project car in my case, if you're serious about a GTA I would echo the words of my local specialist, "Buy the best one you can afford, there's no such thing as a cheap GTA". However, higher mileage does not necessarily mean it's a worse car than a lower mileage, condition and how it's been cared for would matter to me more.
Definitely check the GTA guide referenced above, this one might also give some pointers from a general 156 perspective too -
https://www.alfaowner.com/Forum/alfa-147-156-andamp-gt/1174099-147-156-gt-buyers-guide.html
Hopefully that's a starter for ten :thumbs:
Best of luck with the search.