Easiest solo (imho) of BG1 is with a thief - you can just hide from everything. I got through it all (not ToSC expansion) with only 6 kills by the time I hit the final battle. Some of those kills were not even necessary.
The reason I say "easiest" is because of the sneaking - you don't have to fight much so you never have to worry about a big fight, like in Tazok's tent or a group of mercenaries or anything. Run and hide, man.
I also followed the fastest path, doing almost none of the side quests for experience. I did a few side quests which did not require kills (by the way, if anybody else wants to try this - the enchanted chicken quest requires 2 kills - doh!) Be sure to steal Algernon's cloak and charm the pants off the Sword Coast! Make others do your dirty work!
Now, if you want to squeeze more out of the game and walk around and see things while soloing, I would suggest a fighter type or a fighter/thief. That would make some battles very sweet - use a potion of giant strength, then get in some mighty backstabs! Rawr!