Interesting question. If the waiter or waitress said to me for example, do you want chips or salad with your hamburger, I would say either: "I'll go for the salad" or "I'll go with the salad." I might say : I'm going for a curry" to indicate that I will go out to an Indian restaurant to eat a curry. "go with" is not correct here. Of course, it would be unusual to say "salad" instead as people don't normally go out mainly to eat a salad.

I will go with a salad is the more "natural" sounding of the two sentences.

They both sound fine to my ear, let's see how it goes to native English speakers....