What are all the smaller misc toys in the three baskets? Those sound like large baskets, and to have 3 full of small toys.. maybe you could pare those down. The other items: puzzles, shape sorter, rings, blocks sound good. Just remember that they're all composed of smaller pieces, so that, combined with three large baskets of small pieces can make for a perceived bigger mess when scattered about. The nice thing about the blocks and puzzles and stuff is that the small pieces can be easily contained, and within a specific location, if that makes sense.
For my ds, all his small toys are part of sets, so they are stored separately in small containers that he can manage.. I use little sand-pails.. one keeps foam letters, one keeps lil cars, one keeps wooden shapes. They hang on pegs at eye level and he can easily grab a container and play with it, and it's easier than one big bin because he can easily find what he's looking for. Larger toys like puzzles sit open on a bookshelf, one in his room and one in the living room. I guess I really don't keep small misc. toys.. we're into sets.. ds likes to pile and line up like things.
I'm also working on teaching ds to clean up.. sometimes he does it, sometimes not, but he's catching on that if too many toys are laying out, it's hard to play, and he'll pack up a sand-pail and hang it up before dragging out more.