I've had too much experience with toy management over the years and found a few things that work well.
First - less is more! Sort through the toys and put 3/4 of them away. Yes! That many of them. Out of sight, out of mind in a closet or garage or attic or wherever. Then every few weeks, put the toys away and bring out a few more "new" ones. Your kids are young enough that it'll be like getting new toys every few weeks. They'll actually play with them... have you noticed they don't really play with the tons of toys that are sitting out? My advice is to do this when they are sleeping, though, or you'll hear the 3 year old cry "but I LOVE that toy"... to every single one you try to put away. :-) If a toy has sat in the closet for 6+ months and no one has asked about it, you could probably sell it without much fuss because they've forgotten about it. :-)
Remember that in 1950 the average 5 year old had 5 toys. Yes - 5 - and they were happy. And they had to use their imagination (open-ended toys are the best). At any one time, we have 3-4 toys in our family room - the rest are either in the basement toy room or in the (locked) closet of the toy room.
Second - bins are best but NO LIDS. Kids hate putting lids on and it's harder to see what's inside. It's easy to toss stuff into bins when cleaning up. Toy boxes are good for the big bulky things like Little People sets but small toys get lost in the bottom. IMO, shelves are best... bins sit on the shelves and the bigger toys like Little People sets just sit on the shelves.
Other random ideas.... over-the-door shoe hangers (with clear pockets) are good for storing things like matchbox cars and Barbies (ours are inside the bedroom closet doors). Make some toys supervised toys only.... things like puzzles, crayons, markers, play-doh, board games, etc -- stuff with either lots of pieces or is messy. We have 2 of the white 'towers' with 7 clear drawers (4 small, 3 big) you can find at any store like Wal-Mart or Meijer for art stuff. Everything gets a drawer and it's labeled... crayons/markers, coloring books, playdoh, workbooks (1 for preschool/K, 1 for 1st/2nd grade), color wonder, paints, general craft drawer, plain paper/construction paper, etc. If the drawer is full, we don't buy anything else or we toss... otherwise we'd end up with a mountain of coloring books.