Griffith is where I started as well. Then I moved to Shanker. What's great about Shankar is that it can be studied at the undrgraduate or graduate level. The transition from Griffith to Shanker, for me anway, was a little shaky, at first, because Shanker introduces axioms about vector spaces and so forth. So Shanker is mathematically, a little, more advanced.
Sakuri is a more modern introduction, but not an introductary book. However, I've always heard how it's an exceptional book, and there is a new edition.
I've heard Townsend's book is quite good also.
There's another introduction book titled Quantum Mechanics "A Time-Depedent Prespective" by David J. Tannor that focuses on the time dependent Schrödinger equation, as opposed to the steady-state Schrödinger equation, and the use of wave packets. This book focuses more on the experimentation aspects of quantum mechanics.
Either way, Griffith's book is the most accessible book to begin with that I know of.