Mastodon getting some attention is actually pretty good. It's one of the first times in a while where an online social media network is largely free from corporate control. The code is free and open, and there's no algorithm pushing ads and PR - just a chronological feed of people you follow. And it's definitely more hospitable to leftists than Twitter is, since leftists will always be able to host servers and moderate them.
Hopefully more leftist servers come about, but in the meantime, you can find any server that has a decent description and rules and join that. I recommend sorting by uptime and open registration.
I too am kinda looking for a cool server to get on. I used to be on radical.town, but that server has been defunct for a few years. This is another thing to be aware of on federated platforms like Mastodon or Matrix. It is just as easy for a server to come down as it is for one to go up. It can happen from the admin moving on with their life, getting burdened by other shit, overloaded systems, or neglect. There are plenty of active, well maintained Mastodon instances, so this isn't like a chronic problem or anything, but it is a good thing to be aware of when shopping around.
Unless you are actually following anybody, You are going to basically be stuck with the "firehose" feed. There is a local one (just your home instance) and a global one (every instance in the federation). The local one may be chill if you are on a small instance, but if you are on one of the flagship instances it is basically indecipherable. Same goes for the global feed. It is really important to find people so you have a more curated, manageable feed to look at. I suppose you can do this by searching hashtags, following people who sound smart, then unfollowing the ones who say something incredibly stupid a day or two later.
As a Twitter user I never used hashtags and barely ever tweeted myself. I was a fulltime reply guy. I just followed interesting media people, chimed in whenever I could think of a clever one-liner, and posted pig poop balls where it was warranted. For me, Mastodon would be an adjustment. Most of the journos, activists, and academics I follow have not made the switch. For better or worse, Mastodon is more like this place. A bunch of weirdos and nobodies, except at least here we've got a good rapport.
As far as preferred servers go, it's my understanding that there is a lot of Reddit style radlib sectarianism going on. Mastodon gives instance admins the ability to set their own moderation policy (which is cool and makes banning nazis very easy), but that doesn't mean every admin is a good moderator. As you already can see, opinions vary from "Jessica Ashooh isn't going far enough," to libertarian absolute free speech, to weird leftist sects. I'd love to hear a rec myself from someone who is more settled in. I tended to prefer the smaller (5,000-10,000ish user) instance feeling over the colossal flagship ones. Keep in mind, you can still follow and interact with anybody regardless of which instance they're on.
For servers, kolektiva.social might be the best bet right now
For anarchists. Based on this:
I imagine many users here would get quickly banned.