A toy box sounds like an excellent project and I hope you will keep us up to date on the progress. It would probably be best to just go to the local big box store and invest in some of their common materials for this. I would like to see you have some early success for you and your family to enjoy while you develop your skills. A lot of folks jump into a project where the details are far beyond their skill levels or are beyond the capability of their tools and become disillusioned. The idea is to challenge but not wear out the joy.
If I were you I just go with a simple box of my own design or pull some pictures off of the internet to help me out. Working out the details would be a good learning experience, as opposed to simply taking a packaged plan. You do need to look into lid closure hardware to protect those little fingers.
You can use a jointing sled with your table saw, along with a plane to, get good tight joints for glue-ups. The tooth size-count-per-inch and sharpening configuration should tell you whether the Disston is set up for rip or crosscut.
I normally use diamond stones, oil stones, ceramic files and stones, and metal files (for saws) for most of my sharpening and use MDF and a couple of wheels (cotton and MDF) on my drill press, charged with compound, for honing. It all depends on what I am sharpening (as opposed to shaping). A lot of folks love water stones. You can invest a lot in sharpening supplies and there is a lot of discussion out there on what is preferred or what is cheapest , long term and short term. I would suggest you investigate the “scary sharp” method due to the fact that it works, and has a low initial cost. There are a lot of good videos out on this and the materials are widely available.