I highly recommend NOT sticking to 9x9 and 13x13 board games until you’re “ready” – which is an arbitrary boundary since compared to pros we’re all total idiots and noobs so we’re never “ready”.
I’m a big advocate of playing lots of 19x19 as soon as possible. No substitute for experience. There’s a limit to how much you can train fighting skills in isolation on a small board – at some point you just have to jump into 19x19 and learn in practice