Which Europa to buy
A Project is what listers call a Europa which is cheap because it needs lots work to bring it up to driveable stats. A Project may start as a basket case.
A Basket case is Europa which is in bits and needs to be carried home in baskets before you can call it a project.
A Runner is a Europa which can be driven home under its own power and used straight away.
Concours condition is one which is so perfectly maintained and repaired that it can immediately enter contests with a chance of winning (these are a myth and don't really exist except for the purposes of comparison with a runner or project !)
Option 1) a basket case or project.
Option 2) a (good) runner
You really need to decide what you are going to use your Europa for: occasional use, daily driver or Autocross. If Autocross then it doesn't matter what you buy 'cos you're going to change/upgrade/rebuild everything unless you buy one of someone who already uses it for Autocrossing. If just for road use then buying a Europa which needs work will cost twice as much as you think and usually results in you spending a total in excess of 15K dollars by the time you have finished (option 1) - if you buy one which is not driveable it may even be years before you get it on the road. For 15k dollars you should be able to find a fully functioning Europa with no work to do (option 2) - but you have to wait for one to come around. That may take months but when you get it you can drive immediately. If you intend to use it as a daily driver then you need to buy the best fully working Europa you can find. For some people buying and rebuilding a project is the reason for getting a Europa. For others, driving is the reason. The "real" reason is personal, individual, and no two Europa owners have the same "real" reason.
So you make your choice depending on:
Most probably you will fall in love with a particular car and buy it regardless of logic. Try to drive as many as possible first. I (Julian) went for option 2 and bought a fully functioning Special at top price as my work and family didn't allow my to do option 1). I have great respect for those that go the other route (I did it that way 20 years ago with a Spitfire !).
S1/S2 versus Twin Cam
Had a bonded in chassis which is difficult to change, clip-in windows and high "sails". This model was sold in France, the USA and Canada. Renault 16TS based engine with Lotus mods and single down-draft Solex carb. 4-speed gearbox.
Looks the same as the S1 but had a separate chassis (easier to change) and electric windows (no space for a winder handle). Renault 16TS based engine with Lotus mods and single down-draft Solex carb (89 bhp depending on market). 4-speed gearbox.
The Twin Cam (known as Twink)
...sits 1,2" higher on the chassis, no "sails" at the back, uprated brakes (with Boosters), more leg room, more head room. Lotus-Ford Twin overhead cam engine with either; two double-core Zenith-Stromberg carbs in the US or two double-core Dellorto carbs in Europe (105 - 126 bhp depending on version/market). In Europe that Twin Cam Special (126 bhp) came with oversize inlet valves (known as Big-Valve). All US Twinks were Big-Valve (including Specials). 5-speed gearbox as option on Twinks (later standard). 5-speed gearbox standard on Specials.
Which is the one for you ?
The choice between S2 and Twink/Special seems to be a very personal thing. Some people prefer the Twink body. Some people want the extra power of the Twink engine. Some people prefer the S1/S2 "sails" and the lighter car.