re: New android user here...have a couple questions

I use Notific Pro. It works well for email, in particular. If your phone is locked and sitting on the table, when you pick it up, you can get the gist of who is emailing and the subject without having to unlock the phone. Then the screen goes dark again in a few seconds if you don't care to open it. I'm using K9 email, if that matters.

For messages, I just use the stock program... and for this, regretably, it only indicates "new message". Don't know if it would be different if I used Textra, Hangouts or other texting programs, or if I didn't set something up correctly, but being responsive to texts is less of a concern for me than work email, so this works well for me.

There's a free version... I don't remember if ad based or if it's just limited functionality, but maybe worth testing before you splurge for Pro.

There are other apps which similarly display notifications on the screen. If you don't care for this one, search on the Playstore for apps that have to do with notifications, lock screen, etc.