Pickpocket, Sneak, Alchemy, Illusion, Archery.

You use bow when you feel like that is the best option with poison?
And dagger if you think you can close enough?
Illusion for Invisibility and fun with Fear, Charm, whatever?

Or should I perhaps drop Illusion for Conjuration?

And what type of builds are those you find in the Dark Brotherhood that use Conjuration and Destruction, how does that go well with stealth?

I think a 'standard' thief/assasin build would include those sklils and also light armor and one-handed (with dual wielding).

You should definitely take illusion, for the silent casting perk if nothing else. Once you have that, you can use other types of magic with stealth, but before that, not so much. Mind you, stealth bow is so powerful that it's not really necessary.