1. World - moves that effect the terrain (eg Flame and Explosion)
2. Battle - moves that may cause battles to happen (eg Headbutt and Rock Smash)
3. Misc. - moves that don't fall into the above (eg Forage and Heal)
Unless a huge amount of external moves are planned to be added, I think individual toggles per move would be best, as each server might have different needs. I haven't actually tried most of these yet, just read the wiki entries.
My biggest concern is how/if they interact with claiming plugins in sponge etc.
My list of how I see the current external moves
Cut - Sounds handy, especially for removing looted grottos
Dig - If people ran around spamming that, I'd imagine the terrain would look horrible..
Explode - Kinda self-explanatory, a lot of servers even have tnt disabled
Fly/Teleport - Seems fine, except maybe the rare adventure server that doesn't want it
Forage - Important to get shards for moon/sunstone etc.
Heal - Seems fine
Light Fire - A gamerule can prevent fire ticks, but that would still leave permanent fire everywhere
Rock Smash - Seems fine
Thunder Bolt - Minecraft's thunder is audible across the entire map, would quickly grow old with many people online. It's also quite destructive in its item deleting functionality.
I obviously have some testing to do, but I would only want to use a specific few of the external moves on a public server personally.
While I don't seem that happy with the current selection of external moves, I do love the idea of giving your pokemon unique ways of helping. Kinda makes them more than just a way to fly/battle tools.