I have a MK1. The MK2 is the same underneath but the main killer is the crumple zones it has, which if they start to rot are terminal. The MK2 has a nicer cabin and more powerful engines, but for me the MK1 with popup lights was the original I wanted. MK1 and MK2 hard tops are the same and fit both cars. Many parts can be interchanged between them.
MK1 MX5...
Rust - Sills rot from inside out. If you see them bubbling, they are rotten to hell on the inside. Also watch out for bodged sill repairs as some garages weld a plate over them, then paint black to try to hide it. As the plate is welded
over the drain holes it will rot extra fast on the inside. The drain holes are two little holes on the jacking rail at either end of the sill (2 front, 2 rear on each side of the car) - Rod these out with a paperclip...if water comes out then there was been water sat in there for ages rotting the insides of the sill away.
Paint - The mx5 was one of the earlier cars to use water based paint. It is soft and you should expect paint defects. This is fine, just avoid rusty ones.
Import vs. UK - Imports have far less history and more bodywork repairs. UK ones are far more rusty. Buy based on rust. Have I mentioned rust enough yet?

. Early UK ones have no middle brake light in the boot lid. Even if it is present it probably does not work as the cable fatigues where the boot lid closes overtime. An easy fix with a soldering iron and some new cable! Whether you get a UK or a Jap one they all came from the same factory in Japan. The Japs are quite snobby with trim levels and all tend to have power steering, leccy windows and A/C.
Import vs. UK insurance - Imports are often more to insure by £100, but for some people it makes no difference.
Roof - Check it is in OK nick but a new one fitted is only <£250. I have a hard top as I am tall and get a cold head with the roof down. I rarely take the hard top off.
Engine - Completely bombproof. They are a turbo engine without the turbo and are very strong. When cold (especially when sat for a few weeks) the engine has a tappet noise but that goes away in 5-10mins max. The rocker cover gasket leaks but is a £20 <60min fix. The Cam Angle Sensor (CAS) nearly always leaks - A <£2 10 min fix. I helped a friend with buy an mx5 from a moron. I used the minor oil leak on the CAS to knock money off. You cannot see the cambelt, so if there is no proof of it being done, assume it hasn't. If it snaps though there is no damage done as the valves won't hit the piston - You just break down. A new engine is worth £150 tops so don't worry about them - They are cheap because they rarely break.
Engine power - The 1989-1993 1.6 is 115hp and is a raw rev hungry engine. The 1.8 is more a refined and torquey 130hp but is not much quicker as it is heavier. Pick whichever you please as both are good. Avoid post 1994 1.6 as they were a weedy 90hp.
Exhaust - ANY UK model with decat is an MOT failure as of July 2012. Any <1995 import is ok. Many cars are decatted and are WILL pose you MOT problems.
Hood drain tubes - On the underside of the car near the rear sill holes are plastic drain tubes. These start behind the seatbelt tower and result in a wet seat if they block. Run a coathanger down them (carefully as there is a flap on the end!) to clear them out. Only negative is you get a wet seat as the blocked tube floods.
Safety - Early ones have no ABS or airbag, but the car is pretty dire in general in a crash.
Extras - Leccy mirrors and an electrically extending aerial are nice, but are by no means essential. The A/C adds weight and never works as the seals are all shagged. Power steering is nice. Watch out for leccy windows as they often don't work or get stuck mid travel, but are easy to fix as the runners are just full of 20+ years of crud - A simple summer's evening fix with some £5 grease and white spirit. The 1.8 has a better diff (option I think?) than the 1.6 by far.
Gearshift notchy and/or hot transmission tunnel when car warmed up - Buggered seals. A full kit for the gearstick can be had for <£50 to make it nice again. Very common fault but only affects smoothness of the stick!
Stereo - There are peanuts to buy so ignore the stereo tbh. Jap cars have the all-in-one 'tombstone' style seats with headrest speakers - The speakers will be blown but I replaced mine with JVC ones which made a lot of difference. (Side note: Many bolsters on the driver's side are worn. I removed the covers and have them a wash to remove 20 years worth of dirt, got the mother to fix the bolster and put the seat back together - Looks good!).
Tax - All are the old system maximum tax bracket - £230 ish.
MPG - Both 1.6 and 1.8 overfuel to ensure the engine does not knock (no knock sensor on the MK1) and expect 25-30mpg.
Tyres - Blackcircles fitted midrange Dunlops on mine all round for £220. Cheap and cheerful. If you have OEM 15" alloys this can be even cheaper.
Headlights - The popup mechanism almost never breaks and as such they are very cheap second hand. Certainly nothing to worry about.
I am an engineer (yes a real one!) by profession, but am pretty poor hands-on. I have done loads of my jobs on my mx5! If you break something, who cares when the part is a fiver from the Nutz forum!
Now is the perfect time of year to get an MX5 as they at their lowest cost. I bet Jan will be even better when everyone's Xmas credit card bills have arrived!