45 degree corners are you friend,, if you can get them perfect.

Long clamps and glue,, I use Weldbond white glue,, never failed me yet!

Using a brad nailer is good,, Biscuit jointing is the ****! If you can afford a Biscuit jointer router and the biscuits are not cheap either,, but you'll have a joint that's bullet proof!

Screw and glue requires (in MDF) pre drilling, and if your finishing, and I recommend anyways, counter sinking. Screw and glue will give you a strong joint, but you might bow your wood in the screw area.

You can also recess your joints (dato) joint is what's it's call I believe.
commonly used in shelving, and super strong as the one piece locks into the other, glue, nail or screw.

As mentioned, if you use glue and you have some gaps, you're going to need to sillycone to fill,, or if you use PL off the start, it;ll fill the little gaps you made.

But,, if you take your time, measure twice, cut once, use sharp tools and have a little know how, you should come out with a nice product.

If you like the way your box sounds, you can always coat the interior of the box with fiberglass resin. It'll soak into the MDF and seal the whole box up, and provide another layer of stiffness. You can re-inforce the corners with matting or cloth if you want, but essentially, by coating the interior of the box with resin, you'll make a box in a box, and it'll smooth too.

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