I don't think there will be any official first mate in the story, whether it be Zoro, Jimbe, or someone else (though I do think Zoro sort of has that role spiritually, because he was the first member to join, his scene with Kuma, a couple parallels with Rayleigh, and has been called Luffy's second in command by others.) The Strawhats are a tiny crew, so any sort of structured chain of command outside of captain seems unnecessary. And a lot of them have been shown in some authoritative capacity - Nami knocking sense in the guys, Zoro scolding the weakling trio, etc. I think it would throw off that dynamic to have an official structure. It also seems weird to me that they would go so long without having a first mate, and then have the most recent addition take a commanding position over them.
I think Jimbe will be given perhaps more respect, but I just don't see him being first mate. There's a lot of things he can bring to the crew - his water abilities, his experience as a veteran, his strategic thinking, diplomacy (as someone above said). I don't think he needs an official title.
@auem:
see it this way..even Roger took apprentices like Shank and Buggy…and no matter how courageous Shank was from his early age,he was a weakling too considering the enemy level at NW...so Momo can be Strawhat's apprentice....:happy:..also Momo has a dragon power,who knows what potentials lie in that...
only problem is he has yet to show any interest in piracy...
Shanks and Buggy looked in their teens - older than Momo at 8. Also, Roger's crew looks to be considerably bigger than the Strawhats, where they could reasonably be looked out for, and not every member I think could be expected to have monster strength. And Oda wasn't writing fights for them, like he is for the Strawhats. There are plot reasons for Shanks being on Roger's ship, and there are plot reasons why a weak 8 year old shouldn't join the Strawhats.
@Gizmo:
Think the best alt. theory is the one involving Blackbeard's crew being the anti-Strawhats do the two crews will match in # size by the final battle (and they currently have 10/11 if you count Stronger. And though I don't see any benefit in Oda adding people post timeskip for Blackbeard when he could've added whomever he wanted during the Impel Down raid, that's also a possibility).
We know that he's chasing after powerful Devil's Fruit users. I think it'd make perfect sense if he chose to ask at least one to join rather than take his power.