I am not sure whether I can answer all of your questions, but I will tell you a little of what I know. The Mini Mania site is a great place to gain knowledge and locate cars for sale worldwide. There is also a wealth of knowledge on that site as well. Just like the early 911s, the mini cars also suffer from lots of rust. they are really easy to rebody though, so you will want to delve into the car's history to see if that has happened. Also, the cars have to be 25 years old or older to import into the states. To get around that, some importers have been known to switch VIN tags on the newer cars and later Rover Minis to title them as older cars. I think that once they are here and have a good title, then that ceases to be an issue when retitling. I personally would like to have an early 90's mini and that would be the only way.
You have a couple of different body styles too. The Mark I is the early body and has external door hinges, sliding side windows, small tail lights, and a different grill (looks kind of like a mustache) among other small things. The Mark II started somewhere in the mid 60's I think and has internal door hinges, roll up windows, larger rectangular tail lights, and slightly different grill. Depends on what you like.
The Cooper 1275S is kind of the holy grail and worth a whole bunch of money. The base models came with various motors starting at 885cc I think. A common motor is the 1000cc model, but is still pretty under powered. Pretty easy to change motors even to later rover 1300 efi ones. Most cars have been modded in some form or fashion, so you have to decide what you want - originality or someone else's taste. Some are done very nicely though. Wheels are something you should look at also. 10" are standard and have the classic mini look. A lot of guys upgrade to 12" and even 13" which is part of the "hotrod" package on the 90's Mini version. I sort of vasilated between the classic 10" versus the 12" - still not sure which I would go with. Some cars also had the small black flares (for the life of me I can't remember the name - Weldwood or something like that) and those look great IMO. The hotrodded later version with wild flares and 13" wheels are not my cup of tea, but others really like them. Can't remember that package name either, darn it.
There is a lot more to learn and what I listed is only the tip of the iceberg in terms of differences (and I am going from memory here). I was hot on the trail of a Mini some years ago, but decided to go in a different direction. If LHD is your gig, then the Innocenti Mini would be the hot ticket. It even had better gauging and creature comforts that only the Italians could do in a very basic English car. Pretty cool looking IMO.
Good luck and check out Mini Mania for lots of info.