Besides the cross-hotbar setup, there are some settings that can make targeting with a controller a bit easier. To get better control over what targets your left/right buttons cycle between:

You should check one or the other (not both) of the boxes:
Character Configuration -> Control Settings -> Filters -> Enable Target Cycling
or
Character Configuration -> Control Settings -> Filters -> Enable Customization

The first lets you configure two settings according to whether your weapon is drawn or sheathed. Or the second lets you configure up to four settings you can alternate between manually by pressing L1 + one of the right-side face buttons. (Someone who only plays tank or DPS can maybe do ok with the drawn/sheathed pattern. For anyone who alternates jobs or plays healer, and so may want to at times target friends during combat and at other times enemies, I'd recommend the four manually controlled filters.)

Once you have customized filters, of either type, the left and right controller buttons will cycle only between targets matching your current filter.


Oh, and apart from those filters, up/down cycles through your party list, and L1+ up/down cycles through your enmity list. (If you want to specifically target the enemy with the least or most health, or for tanks wanting to grab the one they're losing enmity on, going by the enmity list is often helpful.)