10mm plywood or MDF for the box, then either paint finish or perhaps Rexine for a vintage look.
Assuming you're not interested in battery power, then any small, say 10 watt, Class D amplifier board from eBay and a suitable power supply will work. Crossover can be as simple as a single capacitor and inductor, or as complicated as you want to make it, but as the end result is hardly going to be HiFi, I suggest a simple crossover is adequate.
You haven't mentioned what source(s) you're going to use, so the input side of the project needs more definition. At the very least, you'll need a volume control and I suggest, tone controls so one of the Vellemann preamp kits should work.
Your most difficult decisions I think will be in the choice of the drive units, and what facilities the project needs to have. The choice of electronics will be relatively easy.
S.