Well....what do you want to do?
AoE carnage or slooooooow single target dmg?
If you are into ST then BS or EM would be your choices, in fact that BS has parry which makes it easy to softcap your melee defense.
EM is for burst dmg only, but after the "great nerf" it is not as good as it was before, but is is pretty solid for taking out enemies with less shots.
ELM is the one for real AoE carnage!
Starting with Lightning Rod (which does not crit and does not get you out of hidden status) and Thunderstrike afterwards which then crits!!! it is really fun to tear whole groups of enemies apart 
All 3 go fine with Nin but I prefer ELM as I really really really like the massive AoE dg it has.
This is not for PvP (maybe someday) and is paired with Ninjitsu. In your opinion, which is better/most functional and fun of the three and if you can answer, why?
but most of the threads I do find aren't very straight forward on the answer I'm looking for.
I have used the search function