In regards to becoming a better player, I would concentrate on playing shorter games, rather than 3-era marathons. Once you are twice the size of the next largest faction, the rest of the game is just mopping up, imo.
As for using a mod, I would give it a shot at least. Version 1 of the Medmod deals exclusively with balancing and AI improvement, without adding new units or factions, so I would think anyone would enjoy it regardless of their experience or skill level. It corrects a lot of bugs, and makes the game more enjoyable in general while you are learning. Versions 3 and 4 throw a lot more at you, so you might want to wait a little while before delving into them.