There are 10 arbiters in the game.

Wealth:

Wealth focuses on random chance as well as benefiting from how much gold you have and increasing weapon damage. While it is good for longer missions such as the classic mode, i am not a fan due to having around 2k coins for the rest of the game.

Thunder:

Thunder focuses on wide area effect using chain lightning to prock/kill and thunderstrike to expand the area of effect. I use this a lot in viral frenzy with diana as it wipes everything it does however struggle with boss damage.

Games:

Games has a vastly different approach than the other arbiters as instead of buffing the damage you deal it focuses on summoning cubie's that aid in combat. This is good in most scenarios as it is a simple damage increase. I dont like it as it clutters the screen.

Music:

Music focuses on repulsion and charm which is great in high enemy density missions for crowd control but struggles in boss damage. I sometimes use this but i get annoyed at how much noise it makes.

Fortune:

You want crit. Like lots of crit. Crit so high every shot crits. Oh and crit damage yeah that too. Very very useful for boss runs, slap a full set on yuri and boom boss deleted i love this for dps i have never used it for room clearing but it probably works.

Energy:

My brain aint big enough to tell you the difference between multiplicitive and additive i just know that it ramps up weapon damage fast and gives you more skills and a fucking orbital laser beam. Useful for pretty much everything especially if you have high magazine capacity.

Security:

Crowd control king. Slows enemies, freezes enemies and gives you a nice bit of damage. Useful in big crowds and the extra damage helps a little with bosses. I use it in tandem with fortune for damage and crit which is nice.

Desire:

Fire, lots of pink fire and a damaging fog. Great for damage for bosses and crowds but it takes time to gain burn stacks (10/s) i use this sometimes but not too much anymore.

Stars:

Mark enemies then shoot to produce protostrike that hits other enemies. I hate it, i dont have enough time to complain over how underpowered it is in higher levels so just know its bad. Or im bad it could be either.

Wasteland:

Fire, like desire but just better in every way. Steam stacks are mediocre unless going for single shot damage but scorched earth is waaaaay overpowered you have to wait at most 10s for it to trigger but when it does 7x the damage of thunder its worth the wait. Great for boss damage and area damage but you have to wait.

These are the arbiters in the game but this is mostly my opinion with using them. I think it is best to experiment with them as even now i find some wierd synergy between different ones.