I doubt that 3.93.1 will be better. 3.93 was supposed to be a fix for an obscure bug which caused LAME to crash or something (plus you could now use LAME on several other OSes), but if I remember right there were other bugs introduced into 3.93 affecting the sound quality. Who's to say everything is fixed in 3.93.1? I believe the output of 3.93.1 to be a bit unstable, but anyway, you can find out for yourself if you do some listening tests. I just stick with 3.90.2/3.92 for serious encoding (and 3.94 alpha for the occasional testing)
3.90.2 is kind of Dibrom's version of LAME. He spent a lot of time tweaking it and making sure every preset gave very good results. In other words, it's a seriously tested version of LAME and known to do what it's supposed to do (as opposed to 3.93.1 - where little is known).
Anyway, 3.94 (according to what I have seen on this forum) seems to have undergone a lot of testing. Though it may give you some high bitrates now and then, the quality shouldn't really be that bad - it might even be that it gives slightly better results than 3.90.2 (depending on what switch/setting you use) for all I know.
BTW, I believe that if you'd bother to read the sticky in the MP3 forum about which LAME version is the recommended version, you'd probably found an answer to all of your questions.
Lastly, if the MP3 format isn't a must for your archiving, try
Garf's tuned Ogg Vorbis encoder (quality 6 or something like that) or MPC (quality 5 / standard)