I use mautrix. It creates a matrix space where all your discord stuff goes, and within that it will create spaces for each server you manually choose to bridge.

DMs also go into a DMs space. DMs are bridged automatically, but each server you want has to be added with a command.

Looking at those three, appservice is old, and out of your element does not do puppeting (meaning it bridges discord-matrix chat rooms, rather matrix-discord accounts), making mautrix the best option IMO.

If you are looking to make a discord server you run accessible on matrix, out of your element may be better.

For using your own discord account through matrix, mautrix is the obvious choice.

Using Mautrix and appservice, both are good enough for me to talk to my Discord only friends and not have the app anymore