Yes, if that kind of versatility interests you. Every class except your highest leveled one (main class) will gain a 50% xp bonus so the game encourages you to branch out. It's up to you how you want to approach it, although most only invest in 2 or 3 classes from the beginning and fill the rest out later.

I would be careful about your armory and inventory space as it can be somewhat limited. You'll most likely to run in to that problem at higher levels when you get class- or job-specific armor though. Weapons are not often an issue unless you're saving your old ones.