Eq for sure, but you might want to consider the 7hz zero or truthear hola for the future

The 770s have flat bass, so there's no extra umph that most people have gotten used to. That's why I like the k612

That's the 770s! If you want something a little more fun while still being decently neutral I'd suggest the akg612s

Are you deadset on Bluetooth? For a budget you'd be surprised how good wired earbuds sound.

Absolutely