I'm a big fan of distributed and federated services but I'm not sure why we need Solid. But since it's not even in alpha state it's probably too early to say.
Quite a lot of distributed and federated services already exist and Mastodon is the youngest among them but it's getting a lot of traction lately - the older ones are Diaspora, Friendica, Hubzilla. They are all interconnected so choosing one largely depends on what additional features you need and which interface you like best. Key is that you yourself or (preferably) a group of friends host your own server. Hosting Mastodon is not that easy though, so I would recommend to start with Friendica or Hubzilla. To start out, you can also look for an already existing server but that's not really the way it's meant to be used. I'm on Mastodon and on Hubzilla (both hosted by clubs I'm working with), but I'm not a social media kind of person and mostly inactive.
I'm a heavy user of Matrix/Riot, which is a federated chat/voice/video conference system. Last year it was adopted by the french government to replace all of their communication systems so there's a lot of development going on. Its not difficult to set up but kind of resource hungry, so don't try it on a shared webspace. If you want to start out on another persons server don't take matrix.org if possible - that's a test installation that has grown hugely out of proportion. Big is not beautiful in distributed and federated services.
Edit: I forgot peertube. I did not manage to achieve anything there. Servers seem to go up and down at random.
I'm not sure why you mention signal.org though. Signal is a centralized service running on only one server and it is only partly open source. Signals author definitely has merits for writing important code but he is an opponent of distributed and federated services. Signal is of course obviously better than Whatsapp.