Rajacat,
Having never built anything like your stands, how did you go about it? Are they simply glued together? Where do you get those kinds of materials? Etc, etc...
JLM's suggestions will get you there.
I shouldn't assume that everybody has a tablesaw in their garage.
You could use plywood instead of MDF; its a lot less messy. However, ply is more difficult to finish.
I used a router, tablesaw, a few clamps, yellow glue and a brad nailer. I simply cut the wood to size, applied glue to the edges, clamped a butt joint in position and used the brad nailer to secure the joint. I did each butt joint one by one until the box was complete. The brads act as clamps. The glue provides the strength. Carpenter's glue is very strong. No screws needed so there aren't a lot of sizable holes to fill.
The base doesn't necessarily require a router. You could get by with judicious use of sandpaper. No need for blocks in the corners. Light filling will be needed.