What is the reason that some people prefer an esrog with a gartel?
If one has more than one esrog in order to fulfill different opinions – when does one use the different esrogim (ie during brocha, Hallel, Hoshanas)?
An esrog with a ‘gartel’ (a strip in the middle that becomes thinner) is preferred by some for its beauty. In addition, there are records of ancient esrogim with a ‘gartel,’ and this is therefore proof of the esrog’s authenticity and purity.
However, most esrogim (even those of good lineage) don’t have gartel’s, and the hiddur is not mentioned by poskim.
For the berachah, take the esrog that is most mehudar in its kashrus. I’m not sure which shittos you mean, so it’s hard to answer beyond this. The esrog for hallel and hoshanos should also be kosher, of course.