I'd stay away from the 924. Basically, here's the deal -- they are underpowered and not worth much. The 944 is a better performing car in every respect, and it's not much more. The 924 was designed by VW, and the 944 is much more of a pure Porsche. While structurally it is very similar to the 924, it is wider and more aggressive.
The 944's engine is a slant four -- not a VW unit, rather one half of the 928's V8. It is gutless below 4000RPMs, but once it reaches 4500RPM, hold on!
Handing is outstanding on the 944 -- and the larger wheels/tires make it better than the 924. It is an easier car to drive hard than a 911.
The other option is a 928, which is more GT than sports car. I happen to think they are fun and very comfortable.
In terms of pricing, you can pick up a 924 for under $1000, and I bought an '85 944 for $850. With a starter and a clutch slave, it was a good runner. (Cost for both parts $200 combined.) Late '85 was an interior change, so post 85 1/2 cars are worth slightly more. But $2500 for a 944 is not uncommon. Turbos are still much more.
928s can be had for under $5,000 now.
Here are the issues: 944s - TIMING BELTS, TIMING BELTS, TIMING BELTS. Kids buy these cars and neglect to change the belts. One day BOOM, the engine is toast. With fluid changes and timing belt changes, the engines can last 300,000 miles. Transmissions are notorious for trouble. Besides being very rubbery, they'll wear out -- especially third gear.
928s have fuel pump issues and electrical issues. Can be very costly to maintain. My buddy bought a "good running" one for $4500, and within three months had another $5000 into it. Interiors are expensive to put right, and dash covers seem to always split.
I'd vote for a good 85 or 86 944. Fun rides.