What difficulty level should I play? I played Civ 2 when it first came out, a long, long time ago... so I'm not a complete newb, but I've forgotten most of what I knew from way back then. I've been playing at the 2nd difficulty level, but it's going slow and I keep getting my butt kicked. Should I stick it out or re-start at the easiest difficulty and just get used to the game then come back to the harder level?

Just stay at the level you are at. You will soon get the hang of it.

Start at the beginning, and play some at each level.
What you knew, counts for not a lot now.
More of a question, is which Civ attributes. Now that'a a puzzle.

For what it's worth, I've played all 3 civ's but I'm a firm believer in starting at the bottom with a new game. And Civ III IS new and different from its predecessors, in many ways. My experience with III so far is that level 2 (Warlord) is significantly more difficult than level one. Not impossible, just more difficult. Good luck!