Definitely best to keep everything on the one character - not only will you have the unlocked content, access to your own little stock of Gil but also the armoury bonus from your higher level classes/jobs.

Whilst the game does indeed allow alts (depending upon your subscription as some are limited to 1 per world) it is not at all alt friendly as there is no way for you to pass Gil or items to your alts without involving someone in the middle as you can only mail to people on your friend list. This is one limitation I really wish they would remove and allow accounts to mail their own alts but for some reason the devs are against it.