Hi welcome!
I did a lot of research before buying mine, even though I was moving up from a 350Z.
Weak points of note are:
Steering Lock Mechanism on earlier models (around 2009 - 2011 I believe) these can stop you starting the car if they fail, most have been replaced or people just pull the fuse to disable the unit
Gallery gaskets again on earlier models are prone to failure as I think the earlier ones weren't metal.
You can find a lot of info on both searching this forum.
With your budget I'd aim if you can to get a late 2011 model at least, there were some revisions to suspension, soundproofing etc you also get a rear parking camera and TPMS on the late 2011 onwards. There was a slight face lift again (around 2014 I believe), you may be able to pick up a 2014 plus model but it'd be high mileage with that budget, I just had a look out of curiosity on autotrader myself and there's a 64 plate 370Z (base model though not GT) with 105,000 miles up for £11k.
Hope that helps a bit, but my advice is to have a good read on the forums!
B