Video transcoding hits the CPU hard. If you hear the Macbook fans kick in during playback, then there’s a good chance you’re transcoding, as the CPU is probably 90+%
To see if you are transcoding, look at the Dashboard via Plex’s web interface while you’re playing a movie. It will show you if the video or audio tracks are transcoding.
Plex Web → Activity → Dashboard
You can use the Plex for Mac or Plex Media Player clients in addition to Plex Web.
This can sometimes happen if there is a poor network connection.
Check your local network (Your Internet speed does not matter when streaming locally).
Check the wireless signal at the Apple TV (if wireless). If feasible, connect the AppleTV to the network via an Ethernet cable.
Connect your Macbook to the network via an Ethernet cable if possible. FYI, if/when you get a dedicated server, it should definitely have a cabled, not wireless, network connection.
As @tom80H mentions, unless you’re using USB2, the drive should not be an issue.
If you want to test, copy a movie to the internal Mac drive, create a new library and point it to the movie’s location. This takes the external drive out of the equation.