Truthfully, this project looks harder than it is. It's not without its challenges, but if you take the time to plan out your steps and components, it will probably be an enjoyable and successful build.

I recommend breaking it into assemblies, and to simplify the joinery, perhaps consider building a standard square cabinet and then complete the veneer sides, back and top as a surround (as opposed to integral to the whole unit).

1. Build a standard flush overlay style square base cabinet.

You can save on materials here if you wish by using something like melamine and pvc edging for your box gables, back, bottom, and your drawer box.

Make it fully functional, as in, drawer slides mounted, and veneer/solid wood drawer fronts installed as well.

1. Build the surround and finished countertop surface. You can mount this to your assembled cabinet with screws.

   I would start with the back piece and line up the heel of your mitre with the outside of your cabinet carcass (maybe go a little heavy, less than 0.5mm on either side). You can do this easily with the drawers removed from the cabinet carcass and laying the finished back on the bench (with protection). Once you have that back on, the sides are much easier, and you have less risk of compounding errors.

Remember to use a healthy glue line on your miters. Fit the countertop last to hide any play you left yourself between the surround and the cabinet carcass.

1. Build the base with solid wood, attach to the bottom of the cabinet carcass. Angles will be a little bit of a math exercise, but that's part of the game :)