Basically in every view (all movies, unwatched movies, recent add movies, all TV shows, a specific TV show, a specific season of a tv show, or a specific movie or TV episode) there is an option to sync, from that you get
- # of items (or max duration of media)
- all or unwatched
- quality of encode
it works better for TV shows in the automatic selection of media, not quite sure how recently added Movies would work.
In TV i just keep it set to sync either 1 or 2 episodes of the shows i want to watch on my phone. after i watch a show at home (or away), it automatically converts the next episode down the list, and keeps it ready to sync.
for movies you may be better off selecting the movie to manually sync after you add it to your library. you can manage what you sync (both add and remove) from the plex web interface.
to sync you must launch plex on your mobile device. it will then start to sync. Plex must be open for the sync to start, it can continue to sync in the background for a few minutes. This is due to apple's restrictions on apps running in the background.
For a movie sync might take 5-15 minutes depending on the quality of the encode, and the speed of your network.
normally if you launch plex when you get up it should be ready by the time you want to walk out the door.
you can sync outside your network too (either on cellular or wifi at a remote location), but it will be pretty slow since your upload speed is a small fraction of what's available on your network. my TV shows take about :30 to 1 minute at home, maybe 10 minutes away.