It would be great if with the roll over told you how many of the arty you have left OR if you could click it and it would take you to your artifacts on the page with that arty so you could look.

You could check your arti's beforehand to see how many you have on you, add the number of arti's you intend to use to your current times done and stop once you hit that number

Of course you could do that, it's just a pain. This is a relatively simple UI fix that would make the game nicer to play.

i just click on it till it says I'm out of the needed artifact

pretty much. most arti's arent THAT necessary you wont use all of them for a mission.