Congratulations on your new family!
I would agree that IKEA is a great place to start. When my kids had a play room, I lined one wall with the short Billy bookcases. Then, I put baskets on each shelf for the various toys. They also fit some of the larger toys (like all of those great Little People houses, cars, etc). Now, my kids have the book cases in their rooms, and they house books, art supplies, Barbies, lego in the same way. We also got a little table that went between the bookcases, so they could craft and play at that. They are great and you can really customize them - doors, different sizes - and they are very reasonable. They are also thin, so that they don't take up too much space and can they can be attached to the wall for safety. This way, you could line the walls with the storage, and still give them lots of play room.