I know for a fact that spinach, collards and cucumbers do well in hydroponics. I've heard that broccoli can be top-heavy and need a lot of extra support. It's also demanding of lower temperatures, which can be tough under high power grow lights.

Most herbs do great - I've seen veritable trees of basil grown hydroponically.

As freemangreens said, root crops can be challenging. I've heard that sand is the best medium for growing them in hydroponics but I don't have any experience with that first-hand.

It's a fun hobby and rather addictive, welcome to it!