Hi Jon,
MDF is a perfectly good material from which to build speakers - it's homogenous, dense, not too hard to cut and glue, and relatively cheap.
If you're happy with a rough/speckled finish then any MDF primer product should be fine, followed by some form a fleckstone coating, and maybe a clearcoat to protect the final finish.
If you're after a gloss paint finish, things are a little more difficult - many MDF primers aren't really that great for this, and you'd be better off with proper spraying equipment rather than cans.
Finally, you could veneer, which, for a rectangular box, isn't too hard. You don't need fancy vacuum press equipment - just get a reasonably flat, thin veneer (perhaps a paper backed type for your first attempt). Spread glue on a face of the box and apply the veneer with a flat plate over the top + clamps. Remove the clamps and plate, and trim the edges of the veneer when the glue has dried.
You can use PVA or animal glue for this, but I've found Cascamite/Extramine works pretty well.
