The least distracting classes would be Red Mage (ranged magic DPS), Machinist (ranged DPS) and Dark Knight (tank). You can't start as any of these jobs until level 50 or reaching Heavensward.

Their rotations are very simple and have no positionals or DOTs. Most of the time they are pressing 1-4 GCD but Machinist and Dark Knight have a lot of abilities to press between the GCD.

You could try healers, where most of the time you press 1 button to deal damage and only heal occasionally when it's needed. There is a DOT to track and at least one other attack you can do sometimes, but they can be the easiest role for some things and not for others.