Kinda new player!

[Niwashi]

I use all three methods depending on the situation. I play on PC, and I doubt much of that applies to gamepad.

The enmity list (or party list for healers) is just as useful on gamepad. (It uses Up/Down buttons to cycle through the party list, or L1+Up/Down to cycle through the enmity list.) If what you want to target is listed there, it's often the best way to target it. It does, however have the same limitations as it has for keyboard/mouse players: enemies who haven't noticed you yet aren't listed in the enemy list and NPCs or players not in your party aren't listed in the party list.

The right/left buttons on a gamepad work pretty much like tab targeting, but can at least be filtered so that, for instance, you can set it to enemy only mode and it will only cycle through mobs without including players, NPCs, minions, etc in its list, or set it to friends only mode to cycle just through players and friendly NPCs skipping over mobs. There are a bunch of different filter options for what to include or not. (I'm not sure why keyboard tab doesn't seem to have the same filtering options. It would make just as much sense there. But I've never heard of it except in relation to gamepads, so I think it's a gamepad only feature.)

Gamepad lacks the ability to click on a mob (or its name), but does have an option to select one with the X button. If you start with nothing targeted (so generally prefix this with pressing circle a time or two to un-target whatever you were attacking last) and then press X, it will target the nearest mob/item/NPC/player in front of you. This works much more predictably than tabbing to the next one since the targeting system so often has a weirdly non-intuitive notion of what's "next". So particularly for melee fighters, this "nearest one" selection is often useful when you feel like yelling at the game "No, not those ones clear over in the far corner. I want to hit this one right here that I'm standing toe to toe with."

[Rinari]

The enmity list (or party list for healers) is just as useful on gamepad.

There are a bunch of different filter options for what to include or not. (I'm not sure why keyboard tab doesn't seem to have the same filtering options. It would make just as much sense there. But I've never heard of it except in relation to gamepads, so I think it's a gamepad only feature.)

I'm constantly surprised how much functionality SE has crammed into the gamepad. The enmity list as a targeting tool has become indispensable for me as a tank, so I guess I shouldn't be surprised that they'd make some way for gamepad to use it to. I'm pretty sure I remember seeing those TAB target filtering options before, so they probably exist on PC, but likely aren't talked about much because we don't rely on it as much. I'll have to give those options a closer look as I start honing my skills. There might be some trick that let's me find engaged mobs that aren't on my enmity list faster.

I should note, attempting to click a mob name for targeting is really more of a last resort for me. If I see a new add, and there are lots of others things around, and the new mob isn't on my enmity list... THAT is when I manually target. Tabbing would take longer than I'd like and those seconds are valuable.