My advice...get a carb engined model. We proved at Santa Pod (the 1/4 mile drag strip) that the 'economy' carb engine does almost as good a job (GLE and GLT finished within a car length, although my GLE had been stripped of some weight), and the difference in economy is significant, especially on long journeys. I've returned 52mpg before, which for a 2.0 almost-sierra-sized car is pretty good going.
If performance is important, even the GLT really isn't that swift (0-60 quoted as 10.5s, 1/4mile in the low 18s), so prepare yourself for an engine swap. Options up to 200bhp are available in a package externally identical to a stock B200E (right Mr Insurance man....

), and information is widely available.
Compared to the 440 2.0, the 360 GLT will be uneconomical, slow, noisy, and will handle (at least superficially) worse. Then again the same is true when comparing it to a Corolla GTi, and I'm in no rush to get one of those either! It's a car full of character, surprisingly practical (the boot of my 360 is easily bigger than that or our V40....an estate!), and which with a little tweaking could have joined ranks of the great hot hatches.
#####
Steve's covered all the bases on what to look for I think, but a quick word on engines...
Although nowhere near the troublesome nature of the 340's Renault engines (he says, exaggerating grossly!!), both the B200K (carb) and B200E (injection) in the 300s seem to have subtle problems occasionally. Even when exhibiting these problems, they'll run more or less indefinitely without reliability issues (to the point where you'd barely notice), but they blunt the performance and economy marginally.
Latterly, something was up with my carb (we think - fitting twin sidedrafts seemed to fix it anyway...

), blunting performance in higher gears. Occasionally it'd sit up and GO on the motorway, but it was rare. When my folks got my 360 13 years ago, it was surprisingly devastating at pulling in 3rd up to ~70. At age 17, most of that was gone. Multiple mechanics blamed engine wear, but a worn engine doesn't use almost zero oil, nor return 138bhp on a dyno with only a cam and twin carb swap! Brand new carbs are available for ~£150, and a rebuild of your original by a professional ought to cheaper.
Injection models almost all seem to suffer with a poor idle, and lumpy running when cold, as well as poorer than expected economy. They still pull like a train (relatively), but something is obviously not quite right. We're working on figuring out exactly what that is...
#####
I'm painting a gloomy picture here, but they're actually one of the most reliable engines in existance, although they like good maintainance. We've yet to hear of a 360 breaking down, let alone an engine dying before the shell does! My preferance would be for the underated (and therefore often cheaper) carb models (GL and GLE), but both are fine chariots with their strengths and weaknesses.
The best bit is you can buy a clean-as-they-come example with change from £300, and with a little TLC go and rescue your friends newer cars when they break down, as well as seriously annoying a few hot hatches with the RWD goodness! Enjoy the hunt...
cheers
James