I think Gandalf's chief purpose in this quest was to rid the world of Smaug, who could have possibly been utilized by Sauron in upcoming wars. There were no "detours" or the such to go look for the One Ring--the path Gandalf chose was the quickest way from Ered Luin to Erebor.
That being said, the Necromancer's presence in Mirkwood belied the fact that Sauron and his minions had some purpose in the North--the Wise may have suspected he was searching for his lost Ring.
I doubt though that Narya itself gave Gandalf any sense of where the One was located. It seems to me that the finding of the One Ring was merely coincidence--"meant to be" possibly, but that's Eru's design and not Gandalf's.
As to why Gandalf wanted Bilbo to accompany him on the quest--beats me.
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