"Linda wanted to go with Jim and I on vacation. Jim and I didn't think this was a good idea."
Do you see the error? For the sake of etiquette, we always put ourselves last in a group (...and I). This frequently causes a syntax error. (Syntax error? Dammit, there's a tax on everything!)
We can easily avoid such errors if we just leave our friends out of it. In the example above, make believe Jim isn't involved at all... leave him out: "Linda wanted to go with [...] I on vacation. [...] I didn't think this was a good idea."
Got it? Linda wanted to go with me on vacation. That means that Linda wanted to go with Jim and me on vacation.
Yes, by all means put yourself last when listing a group, but use the same pronoun you would use if it were just you. Leave your friends out of it.