Hopefully you'll just use whatever language your org/team/etc. uses, and have it compiled to JS or WebAssembly as is most appropriate for said language.
To answer your other question, I most certainly hope we won't see "more Web stuff" built with C++. C++ is a terrible language for that. It's a very good language to do stuff that needs predictable high performance such as games. And games is a good market for C++ in the browser through WebAssembly. But other than that I hope other, more high level languages will pick up.
I guess it will be Rust or Go.
Rust because of Cargo (for npm users a big +) and Mozilla (good marketing of Rust).
Go because of Google (also a Web company with good marketing) and because I read some Node.js developers already switched to Go before WASM.
With that said I'm just parroting some other comments I've seen on this topic in other contexts, so I'm asking the question genuinely.
Why can't the Go implementation can have its own GC, the same as the Go implementation for, say, x86 does?
I'm not a web developer but this has definitely peaked my interest to the point I've been dabbling with WebAssembly. It's really easy to get going so I could see a lot of people with other than WebDev backgrounds getting into application development in the browser.
If a popular web library uses it for something real, they will probably provide a JavaScript API to call into it.
For resources, MDN has a great introduction. Pretty up-to-date too. [1].
[1] https://developer.mozilla.org/en-US/docs/WebAssembly/C_to_wa...
You can program in wasm's text format (the actual assembly language) directly, if you want, and you can program in anything that compiles to wasm. C/C++ have the most developed toolchains for higher (than wasm itself) level languages, for now, but that should open up.