In my experience combining multiple languages usually creates more complexity and is slower than each of them individually because you need to convert the data structures of one language into those of another. Both of them are great languages and I've made web services in both so whatever one you pick will be a good choice.

As for which one to pick, although Rust is my favorite language, if you don't know it it'll take a while to learn. So for this project I'd say to go with Go because it's simpler and you really won't notice a performance difference unless you've got a huge amount of traffic.

If you have any more questions feel free to ask!