Soldier’s Joy is one of my favorites (I’ve now learned it in 3 different styles), also Whiskey Before Breakfast. In a recent jam I discovered that Cripple Creek is actually the song I’m most comfortable playing, probably because it was the first I memorized, even if I play it rarely now.
You mentioned Brodie Buttons, which made me think of Blackest Crow. It’s a really simple tune, great for a beginner, but he plays it differently than you’ll typically find. Normally it’s a waltz, with 3 beats per measure, but he plays it in 4/4 (which is a bit easier to do in clawhammer). It’s another favorite of mine, but I usually play it like it’s written in Brad Leftwich’s Round Peak book, which is the more traditional 3/4 time.
What style are you learning?