With so many to choose from, I'm at a bit of a loss as to which one I should give to Martin. On my previous two playthroughs, I gave him the Sanguine Rose, but I want to think about it this time.

My character is a spellsword, who favours light armour, longswords and destruction magic, and already has rings and amulets sorted. Not really a sneaky type, though. The RP is a bit of a psychopath who's trapped in the wrong universe with no way back, who has a bit of a caring streak for certain people. She joys in bloodshed, but only of her enemies. She'll only allow innocent blood to be spilt if it's either necessary, or if she's just in that mood.

If you want to read more about her mindset, you can do so here: http://www.gamesas.com/topic/1459738-journal-of-a-time-lord-in-cyrodiil/

I previously did it with the Rose as it was easy to get. This time, however, with my character approaching level 40, I believe I can do all of the Daedric quests, if I so choose.

Whatever it is, I never give up Azura's Star.

Definitely. That and the Wabbajack.

It's only valuable if you're playing a character who relies on enchanted weapons. Given that Azura's is one of the few Daedric Quests where you're not required to do something immoral or evil, it's a logical "sacrifice" for a noble sort (even one who might find use for it.)

For the psychopath, I don't see how you can top either Sheogorath's quest or Vaermina's. Hircine's quest could also "fit," if you're not the unicorn-loving sort.

Just to clarify - I'm not looking for quests, I can do those in my own time, but suggestions as to the artifact to give to Martin.

Wabbajack is out, because it's the Wabbajack.

Azura's Star is out - it's quite possibly the most useful of the artifacts.

Skull of Corruption is also out, as the effect really suits the character and I don't think she would want to give that one up. Same with the Sanguine Rose, to a certain extent.

Your character sounds like she prefers blade for melee. . . . Volendrung as a giveaway?

Volendrung! Why didn't I think of that?

Since you're on the PC, if you have the Mehrunes Razor DLC, there's a mod that lets you sacrifice Mehrunes Razor. I think it's the most fitting sacrifice, as Dagon's own artifact ends up playing a role in his ultimate banishment from Tamriel.

If not, I'd say the Masque of Clavicus Vile. It's too weird looking to ever wear.