https://joinmatrix.org/servers/

I use Pragma-Messenger. It's based out of Switzerland. Never seen it go down and I use it daily so i'd call it stable. The site's in German so you may have to use a translate extension in your browser if you don't read German.

https://pragma-solution.com/de/Produkte/messenger

In my opinion getting on the federated messaging train is far more important than what initial homeserver you start on. Technologies like matrix, mastadon and lemmy suffer from network effects and I personally feel like the biggest hurdle is getting over that initial painful hump of getting yourself and the people you want to communicate with all using the technology.

Once you are using the platform regularly you'll have a much better outlook on which homeservers have the users/rooms that you mostly communicate with and you can move there.

I used matrix.org as a home server for years until recently decided that I wanted to support the decentralization and stood up my own instance for me and my close friends to use.

I plan on doing the same with lemmy. I just discovered lemmy today. I have always thought reddit-style boards were prime candidates for federating, but didn't know about this project's existence. I initially had the same hesitation as you when it came time to choose a lemmy instance, but realized it doesn't matter. I just ended up choosing lemmy.world for now until I get more acclimated with the space and then will either stay here, move to another server or self-host.