At level 1, paladin (human only of course) is probably straight up the most powerful, with always-on abilities and immunities. It also has one of or the most difficult ability score requirements to meet. If you include the UA and are lucky enough to roll a paladin with a full noble heritage, you can start with a warhorse and full suit of plate at level 1. Ranger (human or half-elf only) has got a couple very nice abilities that give it some significant advantages, too (chance of being surprised cut in half, chance of surprising the enemy increased, extra damage to most humanoid monsters, on top of tracking). At name levels, both those classes start getting spells, too.

At high levels, monks (only human) are pretty amazing, too. They have naturally improving AC, unarmed damage increases and number of unarmed attacks increases to crazy amounts, plus a laundry list of immunities and special abilities. At low level they are very vulnerable, but if you survive long enough you become superman. They also have very difficult to meet score requirements.

The 1e bard is pretty amazing as well, though it's not even an option until the game has reached around level 10, in addition to needing ability scores similar to the monk's. But the ability to charm creatures as an area effect with your music, at will without restrictions, is pretty amazing. It starts out as a low chance and gets higher as you go, but even if they save against the charm the creatures are will be dazed for a round as they listen to the music. Also being a druid and having thief abilities is pretty sweet.

the most easily accessible power choices would probably be an Elf fighter/magic user or a half-elf fighter/cleric or ranger/cleric or ranger/druid. Full armor, any weapons, plus spells and useful race abilities. Non-humans cap out at 5th-10th level, of course, but if the game isn't going to last that long it won't really matter. You'll only be one or two levels behind single classed characters.

Elf fighter/thief/magic-user is nice, too, but using the thief abilities is penalized or doesn't work by wearing armor, so the fighter's contribution is slightly reduced in that combination. But it is still great to get backstabbing, fighter attack progression and saving throws and weapon choice, thief abilities and spells, and ability to use practically any magic items that are found.

Really, "optimizing" in 1e means getting really lucky when you roll for your character. If you are using psionics, too, just get lucky on the roll for those and then roll the highest power level and power selection. Then you can be a paladin or a monk or a fighter/thief/magic-user that can also start fires with their mind, increase their bone density, have ESP, and potentially kill people with mind bullets.