Your max budget will cover most 944's and quite a few 968's (which some think should be called a 944S3!). My first was a 1983 944 lux, 2.5l coupe in guards red (although the front NS wing was the traditional Guards Pink!). Nice drive, but out run by many modern hatches - and no vertical adjustment on the drivers seat so wife would not drive it. Swopped to a 2.7l 944 16v Ventiler - big mistake. OK, had vertical adjustment on the drivers seat for SWMBO, but unless you kept the engine above about 3.5k revs you might as well have been driving a Rover 1 (IMHO I hasten to add, before I get flamed by S owners!). Swopped that for a 968 tiptronic coupe, initially as our main car, then as a weekend toy, loved it so much we kept it for 12 1/2 years before having to scratch the cabriolet itch - and did that with a 968 tip cab 7 years ago which we still have!.
Big advantage of later cars (I think S2's but am not sure, certainly 968's) is galvanising, so tinworm is far less of a problem. Fixing rotted sills on an early 944 properly could easily be £1000 - 1500 per side!! It can happen on later cars - I saw a 944 cab (not turbo so must have been an S2) in Wendover a couple of years ago, and both sides were totally rotted out wheel arch to wheel arch.
Basic maintenance on these cars is relativly easy - I was able to do an oil/filter/plugs change on the 968 myself, and I'm no mechanic. However, timing/cam belt and rollers change is a requirement every 4ish years (think £400 at an indie), and many think it's worth changing the water pump on the second or third belt change.
Personal opinion - if I wanted to buy a 944 today, the only model I'd look at would be an S2, but within your budget you could also look at a 968 coupe (don't discount the tiptronic, as you can drive it as a 4 speed clutchless manual, the 968 tip box is IMHO better than the 944 auto, and the tip coupe is cheaper than the manual these days!) or possibly a 968 Sport - although that would be at the top end of your budget these days.
As an example, just listed on PH and 968uk :
https://www.pistonheads.c...ort--iris-blue/9721698