I just have my instance installed as a progressive web app with emails enabled for replies. It's a little roundabout I suppose, but my email will give me a notification when I get something.
Sync - whenever it launches. :) Was my favorite reddit one.
Out of the current options I have tried (Connect, Jerboa, Liftoff and Thunder) I think my favorite is Liftoff.
Jerboa isn't compatible with my main instance, but I enjoyed using it as my first app before the others came out. Connect is seemingly slow to communicate between instances/communities for me and I am picky about some of its organizational features. Thunder does a decent job, probably close runner up to Liftoff. Going to keep trying each one as the apps and Lemmy itself develops.