Don't think about the speeds advertised by providers, you'll never come close to them. You seem to require a media server, so give more importance to storage.
From my research comparing HostingBy, SeedHost and Ultra.cc - HostingBy has the highest €/TB rate except for the 1TB box which is ironically the highest €/TB rate
Here's the Google Sheet if you're interested Ignore the remarks and INR part, I'm Indian so wanted to see what I would end up paying
I will add on more providers at some point, but these 3 are the big names with decent prices and support.
As for your other problem of app selection, I don't think you'll find any of those in most providers natively (except for Transmission). You can request them, but its not a quick process. Instead of that, try installing them yourself. Even without root, it shouldn't be impossible, the only thing that may be annoying is you may not be able to setup reverse proxy so you'll need to access those services with http://ip:port