Reddit reviews Mickey Baker's Complete Course in Jazz Guitar: A Modern How-to-Play Jazz and Hot Guitar, Book 1 (Ashley Publications)

For standard swing type big band music it's helpful to learn the basic comping style that goes with. Here's Herb Ellis giving a demo on the style, and you should also check out him comping for Joe Pass on Cherokee. For the basic chord sounds I usually recommend Mickey Baker's Complete Course in Jazz Guitar, Vol. 1. It's not perfect but no book is, and it has diagrams, super basic theory, and costs less than $6.

The thing is, big band music has come a long way since the 1930s, and you may be called upon to play pretty much any style of music, which means you need to not only know a variety of chord voicings but also various comping styles. There's no way to quickly teach that, so you'll need to just listen, study, and ask questions of pro players like you're doing here.