I’ll start with the easy part: If it can handle HTTP, it can handle websockets. There are some subtleties, but they won’t usually apply to rented servers (only PaaS or other forms of application hosting).
My recommendation: Start by running your app locally, and launch a handful of clients (even if they’re all just running on your own computer). See how much memory your app needs. Then figure out how much your rented server will need in total, estimating as best you can, to try to get an idea of what sort of needs you have.
I suspect that a single euro a month is only going to give you a teeny tiny server, and you’ll be constrained by a lack of RAM. But maybe I’m wrong.