I know that if I have too many toys out, that Riley does not play well at all, he just wanders aimlessly from toy to toy, not really focusing or engaging well at all. Here is what we have:
~Book shelf in kitchen with selection of books on top shelf, and 4 toys total on the other two shelves. These get rotated with toys from the closet every few weeks.
~In the living room, he has two little baskets of toys with cars, bears, set of stacking blockes etc.
~In my office, he has books, legos, magnadoodle.
We have a shelf in the closet with craft supplies, such as paper, pens, playdoh etc. We tend to do one of these activites when he wakes from nap every day. He does not have free access to these supplies as he would ruin the house with them if left to his own devices. Although he is getting much better at playing independently with play doh.
So, in your house, I think Riley would get too overstimulated and not play well at all, as there are soooooo many choices.