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.
Started with Jerboa, which was quite nice. Not perfect, but alright. It had more and more issues especially with lemmy version not being up to date on lemmy.world, so I tried others. Connect and Summit were not doing it for me but then I've found Liftoff - and it's great! There were some quirks with setting it up but overall it is real nice, has modern look and pretty much all I'd expect. There are some weird bugs with it though, will see how that shakes up.
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.