I'm father of a 4 year old, and we live a couple of blocks from the library. Seeing how his interactions with the shelves has changed over the past couple of years has been really interesting. At first it was enough to look at the covers and spines, then he could pull himself up to the bins of board books, and eventually started grabbing from the shelves himself.
And like you, he loads up with a little bit of everything (it doesn't matter what he chooses, we check it out) and we take it home to read and see what sticks.
It's probably no surprise that one of the most exciting trips he can make is driving to PDX to go to Powell's.
There's probably a UI genius out there with great ideas for it, but I don't see how anything can beat going to a library in person.