I finally hit BLU 99 a few minutes ago, and used a grand total of about 5 spells (and managed to keep Blue Magic capped, and Sword almost capped) the entire way.
Sprout Smack, Cocoon, and Foot Kick at the start. Head Butt at 12, Bludgeon at 18. Picked up a few other spells along the way (didn't get Auto-Refresh until after 80), but basically spammed Sprout Smack and Foot Kick from 12 to 99, mixing Bludgeon in down the final stretch.
You can explore the world and learn all the spells as you level, but there will be roadblocks (to access some mobs you need to progress through Zilart and Promathia for example, and soloing those is best done at or near 99) so my advice: take advantage of double XP and level simply now, get your Blue Magic skill up, and you'll have an easier time of it afterwards. Keep your Artifact hands handy when you get them, they help for learning new spells too.
One piece of advice: right now the Festival of Swords is going on. Speak to an event Moogle to be given an Ibushi Shinai sword, which has a DMG rating of 1. You don't need to have it enchanted or whatever the moogle asks you to do for participating in the event, just keep the Ibushi forever--it will be your best friend for learning spells in areas you've overleved, as it allows you to feed TP to mobs without killing them too quickly. This sword is only available during the Festival of Swords event (as far as I know), so make sure you grab it!