Let’s start with what tools do you have?  You can build toys with hand tools or power tools or a combo.  Special, unique tools are not required and overly expensive tools are not required.  What is your woodworking background and experience level.  Tell us a bit about yourself.   That will help everyone provide some useful advice.

There is no simple answer to this. It depends on the type of toys you want to make. For something simple like the Play Pals, you need a scrollsaw, a drill press, or some other method of drilling straight square holes, and various sanding tools. The more complex the toys get, the more tools you need.

I think you should add a scrollsaw to your tools. Not only can you cut extremely complex parts that are impossible to cut on a regular band saw, but it can also make internal cuts. Most cheap scroll saws are junk. The lowest cost scroll I would recommend is the Bauer scroll saw that Harbor Freight sells.

 

I have two belt sanders, a Shopsmith 48x6 and a Delta 1x42 belt sander. These belt sanders touch everything I make. I highly recommend the Klingspor sanding mop I use this a lot. I have a spindal sander that gets occasional use, but not nearly as much as I thought it would.