While a lathe is not a must-have tool for making wooden toys, if you plan to make any number of wooden toys or make it a regular hobby, you'll want to consider investing in a lathe to create toys with even sides and smooth surfaces, drill, sander, router, small hammer, saws (template and saber), File. As for the tools you mentioned. You use them to cut metal or pipe, not wood. Instead, look for a jigsaw.
They have their place, but cut wheels are not designed for cutting wooden planks. They are good for cutting only very small items (like 2 mm maximum). These are good for making ruff cuts on plywood, but they are not good at doing detail work. Instead, look for a jigsaw for detailed work.
Table saws are always good, but I think what you bring to the table will not be the best choice for the items you want to make. I would invest in other power tools first. Part of the joy of old-fashioned toys is that you can often make them yourself. However, making wooden toys is not a joke, it requires decent woodworking skills and, of course, a suitable workshop.
What makes a workshop good for a toy manufacturer? We'll see about it. As usual, this was a “fly through the seat of the pants” project, meaning I wasn't working with a formal pattern, so I needed something to work with. I started by measuring the handmade quilt and from there I was able to determine a base for the crib that would be about 9 by 20 inches at the base and 10 inches tall. There are few parts needed for these, with the exception of wheels and wooden axles (the axles eventually stick into place).
Wooden toys are basic shapes that children will recognize, but they lack the detail that would turn them into works of art. While you browse, you'll also find all the wood, tools and supplies to start creating memories for the little ones in your life. Some of my friends had babies recently, so I made more wooden creatures as a gift for each of them. Unlike the typical modern carpenter who uses many large power tools, the toy manufacturer usually only needs fine hand tools.
In Erin Freuchtel-Dearing's book Natural Wooden Toys, she offers plans and instructions for 75 projects you can do in a day that will stand the test of time. To make a wooden animal, draw a silhouette design on a cardboard and cut it out with scissors. As I discovered with my son, wooden animals became the perfect occupants for sensory containers and Waldorf-inspired activities. The jigsaw allows you to make an infinite number of intricate wood designs, but also make straight and fast cuts.
If you think about making wooden toys for your children, get one, and your life will never be the same again because your list of projects will grow tenfold.