I don't have an answer to your optimal game, per se. I think there are some nice combos out there, but a good part of that answer has to deal with the group and their tolerance/desire for game factors. I think for a regular playing group Exodus Ionian can offer an added challenge, but for an infrequent group it's elements may not add up (Like game elimination, extra play time).
A year ago I played a game version I liked at a Con that was Base game, Cylon Fleet, and I think Pegasus Overlay for Cylons ship. It worked well with beginner, kept the cylons happy, but kept straight forward rules, pilots busy.
I played several games this weekend with several people I did not know and I taught some new people. We played lots of vanilla base game - which I ended up likely because it's been a while since I have! For really new people, I recommend they play Pilot and if they are a Cylon, reveal quick. As a pilot, they mostly just have to roll well, maybe scout, and learn the game. If they go cylon, it's easy enough to give them (fair) suggestions until an experienced cylon/sym comes forward. After that, I recommend support or Military that is NOT admiral to start. We had someone who was military, and later they became Admiral (when Adama got brigged) but by then they had seen enough to "get" the basics of Admiral. I think president is the hardest to play, as you have so many cards and choices - which you can't really get help with - it's a challenge for a 1st time player, even a 2nd time player depending on what happened there first game.
Later, we expanded to Pegasus and even when that was a players 2nd game, they were a lot more comfortable with the few additions it brought - and pretty much every crisis was new already… I did not due New Caprica since the games were already running LONG, and that is such a new group of rules. The groups were not ready for Exodus! haha
I say if you can get a regular group of players, you play with as much as you can handle and reliable fit in your time window. If you are in a pick up game situation - experience level, enthusiam, and be clear on what an expansion brings, especially in time and hassle.
I like Holy Outlaws idea of the Cylon Leader for a new person. In a sense it's a Win-Win… no one expects the new person to meet their goal (win), and if they do! (super win). My only concern is it is hard to "advise" them what to do without knowing their agenda… but hey, they are new and probably just thrilled to be playing! And as HO said, they mostly only hurt their agenda, but aren't laming up a team. It makes me less concerned about "starting" with Pegasus version.
If there are lots of new people, I have just "run" the game and not played… to keep it moving, help with questions and advice, etc… not as exciting for me. I have been working on a "demo" game that I can "run" that would rush threw the game in 60-90 minutes to get all the elements out, then start a "real" game… so I would assign roles and loyalty cards, would start 2 jumps in, maybe a cylon reveals on turn one, guarantee a 2 jump, etc. Rules explained on the fly, etc… but get the mechanics of spaces and voting and ships out there.
Any BSG game is a good game…hehe