I like the storage options at Ikea. There are also some good bins at Target. My method is small bookshelves and bins -- large toys (trucks, castle, dollhouse) go on the shelves, small toys or sets (train set, race track, blocks) go in bins either on the shelves or lined up on the floor behind our couch. I use one of those pop-up hampers for balls. Some things I've learned from experience:
don't buy bins that have sharp corners (some at Target do)
Be aware that if your child is a climber, s/he will use the bins as step stools, so make sure they are sturdy and childproof accordingly
There is a "dump everything out" phase that starts around 15 - 18 mos when children will empty every bin you have just for the fun of dumping. It's exhausting, but a good time to teach about cleaning up (I use the clean up song "Clean up, clean up everybody do your share/clean up clean up everybody everywhere").
If you put like things together (all cars in the red bin, all musical instruments in the blue bin) and have some type of system that's easy for your kid to understand, you are more likely to get help with clean up. You are also less likely to hear "Mom, where's my..."
If you don't like looking at all the stuff on the shelves (or want to look less cluttered when company comes over) -- use a tension rod and an inexpensive curtain to cover the front of your shelves.