I don't really count GD as a rhythm game, because you don't even tap to the rhythm of the song most of the time (wave mode and ship mode). osu! was my first TRUE rhythm game.
Does SingStar count as rhythmic game? If not, then it's either osu! or some simple browser flash game that I shouldn't count in, as I played it for maybe a couple of minutes.
Osu, Just kidding, before when I knew osu searching up "rhythm" or games related to music, is that I play mobile games such as Cytus, and Love Live Idol Festival (but the bang dream one is harder one). Right now I am playing a new one which is Arcaea which is a good one to have fun in my perspective.
My first rhythm game was Super Hexagon on PC, it was the first PC game I ever purchased and it ignited my love for rhythm games. Deemo, Geometry Dash, Cytus, osu!, etc.