I know if I want to keep it, I have to go to that mage in the pub...I just don't know what is best? There are so many opinions on this in other sites, I could use some help from this forum.

I somewhat feel obligated to return it to her, but I like the no limitation idea for the star. And I don't know if Aranea is worth it as a follower.

If you don't mind capturing Human souls, then the Black Star is superior in every way. You can trap the same white souls that Azura's Star can, and also black ones (though this is likely a glitch or an oversight).

You get the black star by taking it to the mage and you get Azuras Star by taking it to Aranea. The black star is better because it takes human souls and all human souls are grand size, Azuras Star on the other hand only takes creatures souls so you have to kill a large creature to get a grand soul.

You can keep it if you side with Aranea and Azura.

If you side with the mage, you get an infinite Black Soul Gem. Siding with Azura gives you an infinite Grand Soul Gem, and Aranea as a follower.

Definitely Black Star, but I went with Azura's anyway (because Azura is awesome).

id go with The Back Star because i love it for enchanting, and i already have a http://elderscrolls.wikia.com/wiki/Brelyna_Maryon