Here's my list of useful skills. Combo skills (those that have the red flame marker that show up above your hp and sp bars) are generally bad since there's some bug with them that makes them cost twice as much sp (or maybe it's intentional. Can't really tell.)
Tier 1
- (Poison) Rapid Shot
Bossing pretty much. Highest DPCD - White / Rainbow Peacock
Pierces, shotguns, not too high mana cost. Don't get rank VII of this though, it changes to a 3x combo skill and becomes significantly harder to cast. - Charge Shot
I actually haven't used this yet, but from what I know it's good burst damage and has the longest range out of everything. - Exorcist Arrow
Pretty much a rarer, more expensive and powerful Charge Shot.
Tier 2
- Icicle Arrow / Storm
Good single target damage, really good against things with large hitboxes and has some small aoe around the thing you targeted. - Lightning (Flash) Shot
AoE Piercing, gains additional arrows at ranks III and V. - Arrow Rain / Meteor Rain Shot
Costs a lot of sp and is really bad at lower levels of the skill, but is good if you can take the time to max it out. Skill Force triples at max level.
Tier 3
- Venom Arrow
Single target damage with lowish cooldown. The poison it inflicts doesn't do that much damage even at higher ranks. Strong against Odin. - Cursed Arrow
Single target damage with lowish cooldown. Slow is pretty good if it works. Strong against Odin. - Collapsing Arrow
Burst damage. Bad at anything above rank IV since it gains more arrows which take forever to launch. - Backstep (Arrow)
Gains an arrow per level after rank III. Does pretty OK damage and helps you kite somewhat. - Aqua Needle
Haven't tried this but I think it's pretty bad? - Kicks
Do good damage but are melee.
The rest are situational I think.
Edit: You really shouldn't be using Artemis though, unless you get Exorcist Arrow on it. Greatbows have +5 dex and Fuedou bows are way cheaper to smelt while still having about the same damage.