The thing with table saws, unless you get on with a big table or build a big table, it is quite unwieldy to get a sheet of wood onto one to cut. I find having a flat surface (ie garage floor) to place some 2x4's on then placing the sheet of wood on those and using a circular saw with a fence guide much easier than lifting huge sheets onto a table saw.
With routers, any quality reputable brand will do really. And get a circle jig to attach it to for making perfect circles.
Remember it's the glue that holds the box together. Use of good wood glue is key, and having proper coverage. I just use an 18 gauge Brad nailer to quickly tag the sides in place along with using clamps until the glue has dried.