Well there isn't a path to deviate from until you actually get to the world map.
So here's my first tip: Kill Zidane at the start of the Plant Brain battle.
One of the best battle tips, however, is to set the ATB to Wait, then every time one of your allies performs an action, make sure another character selects something to keep the enemy window open. This ensures the enemy ATB does not rise until the attack is over, putting you at a much better advantage. It makes the game a lot easier.
Sadly, the actual battles of FF9 are so slow; from the start up to the actual ATB build ups, it's definitely one of the slowest in terms of battles. That, and there being no way to reduce/disable encounters are probably the only negatives.