What do you say? You say that you want to convert a desktop app into a web app, and take it from there. The app itself may start to dictate the approach anyway, which we can't speak to without any details.
You'll always be putting your trust in someone if you're not doing it yourself. There's no way to absolutely guarantee what's being done is an effective path, but you can always have development plans vetted by a third party, and it may be worth it.
In the JS world there's always a "flavor of the week". There are several standouts, e.g., React, AngJS, EmberJS, whatever. The back-end isn't as relevant if all it's doing is shipping data to the client (browser), but infrastructure costs and maintenance always matter. It also depends on what the back-end actually needs to do (batch jobs, timed jobs, etc.) but you have a lot of flexibility in this regard.
Feel free to reach out if you have additional questions; I'm reasonably easy to get ahold of.