For soloing, just avoid MNK. MNK's extreme reliance on positionals make it a real pain to solo with.

Contrary to popular belief, you can hit with your positionals while soloing mobs you have aggro on, but it's really rather counter intuitive since the mob isn't actually ever facing the exact direction it seems to be facing while it's "turning toward you". It turns toward you faster than its turning animation displays, so by the time it's looking 20-30 degrees away from you, it's actually already looking strait at you. If you take this into account, and you time it right, you can hit them in the back or flank regardless. But the timing must be absolutely perfect.

If you don't do this as MNK, your solo DPS is abysmal compared to pretty much any other Job. If you don't mind doing it, then MNK could be for you and feels very rewarding when you do manage to hit all your positionals while soloing, but otherwise you're best going with another DPS Job.

Beyond that, pretty much any DPS Job is on equal grounds for soloing. I prefer NIN, myself, due to my love of everything stealthy.