Wood – What type of joint should I use while building a plywood box

Dowels are probably your best bet for this fix because the tool cost is much lower for the case that you need to purchase tools to do this repair. The cost of a doweling jig is much lower than a biscuit cutter. Drilling the dowel holes is easily accomplished with an electric drill.

If you end up with just a one inch wide repair strip added in then I would just drill the dowel holes right through the strip and into the original material on each side. Do check your table top pieces for overall flatness after you separate the two sides from the split. Warped lumber often develops a curvature that spans a greater distance than just one inch. You'll need to take this into account when you decide to start trimming away the split edges.

With properly jointed surfaces on the two trimmed edges and the hardwood accent piece the dowels and glue should be plenty strong to hold things together.

You may want to cut the accent piece just a small bit longer than the amount needed and then trim and sand it to the existing round table edges after the gluing is done. This will give you the greatest opportunity blend the edge of the table to the nicest fit and look.

I see some challenge in clamping the round table to get good tight glue joints. You may need to fabricate some jigs to help provide a place to engage your clamps across the width of the table. The sketch below shows one idea of how to do this. Some flat boards about 4 -> 5 inches wide can have some blocks glued and screwed on the ends that will provide a place to engage the clamps.

I have shown the blocks somewhat offset from where they would actually be attached to the boards so that you can see the nature of how they would fit to the contour of the table edge. Long bar clamps or pipe clamps would be spanned across the table top at the overhang of these boards as shown in the next picture.

Any sheet goods are going to be lacking in strength in terms of deflection so your construction will have to compensate for this. You'll want to create rigidity using geometry of some kind like this torsion box or maybe by adding solid wood stretchers and aprons. As far as materials go, I'd be partial to MDO for a project like this but here's your options.

1. Plywood is the strongest of the sheet goods and takes mechanical fasteners by far the best. But it's either a terrible surface to paint (if you get construction grade) or too nice/expensive to cover up (if you get cabinet grade).
2. MDF paints well but is monstrously heavy, is the most prone to sagging, and will not take fasteners in its edges.
3. Particle board is inexpensive but it's flimsy and is almost impossible to seal up well enough to protect it from water damage unless you cover it with laminate but then you've just got a counter-top.
4. Melamine has an durable, stain proof film on both faces but as such it cannot be painted. It's also susceptible to water damage as it's just particle board in the center.
5. MDO is a sheet of plywood covered in a thin layer of MDf. This gives it the strength and versatility of plywood while keeping the weight down, but it also takes paint just like MDF. It's only draw back is that the edges are not finish grade in the traditional sense so they'll need to be banded or captured in some fashion, and it's a bit more pricey than MDF or CDX.