I generally try to play Artanis as an aggressive engager. Focus on getting displacements with your prism so that your team can secure a kill. Artanis can easily punish an enemy in a bad position; be careful not to overextend, as Artanis has almost no way to disengage unless you use your heroic.

In addition to displacing/punishing enemies, Artanis is also great for laning with Blade Dash (which helps for his quest).

Level 1
If playing a map where your team might have trouble with non-hero enemies, take Amateur Opponent instead of Seasoned Marksman.

Level 7
If your team has a lot of difficulty clearing waves, grab Solarite Reaper.

Level 10
If the enemy team has someone that you need to push out of team fights, take Purifier Beam instead of Suppression Pulse.

Level 16
If you're facing a bunch of chunky heroes, take Titan Killer instead of Blades of a Templar.