It has been shown multiple times with key hints that Zoro is the closest to the captain. Zoro is also like Marco's Whitebeard, as they are both the second strongest of their crew behind their captain. During the incident with Usopp leaving the crew, it was shown very well that Zoro can be level headed during dramatic times, and tell his own captain to pull himself together and act like a captain and make harsh decisions if it ever needs to come to that. Zoro also took Luffy's Pain from Kuma, and this is proof that he cares for his captain very much. Zoro is also the second one to be aligned with Luffy's crew so he is also the oldest one to join.
The only one who comes close in regards to Luffy's underlings is Usopp but as you can see he lacks power and I believe that Zoro completes all the conditions while Usopp lacks a few. If anything, Usopp seems more like a bestfriend than a second commander.