We love puzzles at our house. Our kids first get interested in them around their first birthday. Of course at that point they can't put them together by themselves at all. We got some Melissa & Doug chunky puzzles as hand-me-downs and those are probably the best ones to start with. The pieces are very large and the knobs are big enough to to fit in little hands well. I like the shape puzzles because they help kids learn about shapes and geometry at the same time as learning spacial skills. Of course, my kids love the animal puzzles as well. We have a few puzzles with the tiny little knobs and those are good to move on to after your child gets the idea about what to do with the puzzle pieces.
We love name puzzles. We have one for Naomi and need to get one for Daphne soon. It helped Naomi learn how to spell her name. Plus they are just fun since it is so personalized. We got ours at One Step Ahead but I've seen them other places as well.
Attempting to clean up clutter, I started putting all of our wooden puzzle pieces into the same plastic container. We have 5 wooden puzzles I think. What started out as an organizational tool has ended up being an added difficulty level for puzzles. The girls love putting all the puzzle boards on the floor and then picking a piece out of the box and deciding which puzzle it goes to and then finding the right place on that puzzle.
Sometime between 18 months and 2 years your child will probably be able to move onto other types of puzzles. Of course, their ability to accomplish them may take some time. We bought these for Naomi around 18 months and they were WAY too frustrating for her until around 2.5 years. Daphne can do them some now at 22 months so you have to take your kid's abilities and temperament into consideration. I like these puzzles a lot but the kids don't get them out as much as other puzzles.
Three dimensional puzzles are a next logical step. Daphne is starting to enjoy this one we have. The trick for this one is getting all the pieces into the box to fit, and to stay in, since there are open sides. It is a bit frustrating for her at this point but she is so patient she just keeps working at it.
Melissa & Doug See & Spell puzzles are my absolute favorite. We bought these for Naomi when she was around 18 months and was just mastering recognizing her letters. Now, at 3 years old she loves learning how to spell words. She now looks at the picture of a frog and sees the word next to it and can tell me you spell frog f-r-o-g. Daphne is at the point where she gets excited to find the letters she needs for the puzzle. She'll see an "i" on one puzzle and excitedly says "I need an i" and looks through the pile for one. I highly recommend these. If your little one still likes to put things in his or her mouth you need to supervise this puzzle well since he pieces are a bit small.
The next logical step in learning puzzle and spacial skills is to move on to regular cardboard puzzles. They make tons of these in various sizes. Naomi has a couple with 20 to 40 pieces and loves them. Unfortunately (for me) she needs a lot of assistance. How many times a day do I need to do a Pooh puzzle? Too many. I’ve been trying to work on her logic and spacial skills by “thinking” through the puzzle in different ways each time. Sometimes we start by putting all the edge pieces in a pile and all the middle pieces in a pile and put the whole edge together before doing the middle. Sometimes we just look at all of them and see what fits together. Sometimes we chose a particular scene (for instance, the cow) and put it together then chose another part of the scene to put together. I’m hoping this helps her build those critical thinking muscles.
Then of course, you can move on to pattern blocks and boards like these.