There's a huge amount of spells, but very few of them see actual use. Most elements have 1 or 2 good damaging spells and everything else that gets used is for utility.
Many people have the support spells (Shifta, Deband, Resta, Anti, Megiverse, Zanverse) on their sub-palette. Bouncer's Jet Boots has Shifta, Deband, and Zanverse built in to it's Photon Arts, so you don't need to have those equipped as Bo.
Some other really good spells that you will benefit from having constant access to are Safoie 0 (or ilzonde - these are movement spells) and (Na?)megid 0 (Damage over time around you).
The only class of the three you mentioned (Bo, Te, Fo) that gets any benefit from having multiple different element weapons is Force (through it's skill Elemental Conversion), and you only get a very slight (a few % at best) power increase from doing this, so it's not recommended. Also, Techter's wand can change elements as well.