Pandora-like media streaming server?

If you're using the browser based pandora client for Linux you'll experience quite a bit of lag when resources get scarce. Since you're using ubuntu as a server you may want to take a look at VLC, Plex or Squeesebox/MusicIP/MediaTomb (the last three build upon each other). Plex is the most robust but won't be like Pandora at all really. I use it to serve Movies/TV series and the like. It will also stream music as well but it's also browser based but, unlike Pandora's web client, it's HTML5 compatible. VLC uses clients and may/may not be to your liking but it's platform agnostic and is fairly easy to figure out. Plenty of HowTo's on the Internet for Plex and VLC.

Squeesebox/MusicIP/MediaTomb is a bit more difficult and may not be something to undertake without looking at your resources for the RaPi3 but there are guides out there to lead you along.

That's what I see for streaming services which (in my estimation) are worth looking into. I don't think you'll find a 'drop in' daemon for Ubuntu which fits the bill for what you are used to on Pandora. There are clients that you can use, like Pithos, but those are Linux specific. If you're streaming from your gaming system you'll most likely want to find a Windows binary for a pandora client in order to keep it as minimal on the resources as possible. If you're gaming using Wine on Linux then Pithos may be the client for you.