Most of this is determined by the weight restrictions in your area. It's different in pretty much every state. For example, here in IL, we use the federal bridge formula and we can only have 4 axles on a single vehicle. Even so, you get so little weight with the 4th axle that you almost never see them here, it's all tandems. To haul more weight we use semis with short dump trailers.
Now, in pretty much every state that borders IL, they have an exemption to the bridge formula that allows them to carry more weight on 4 or 5 axles. I know in Wisconsin you see 4 axle dump trucks everywhere.
In Ohio they can have as many axles as they want and you seen 6 and 7 axle dump trucks there grossing 80,000 legally.
Beyond that, it depends what you want to do. If you want to haul concrete, you'll want a steel box or tub. If you only haul stone or dirt, aluminum is fine. If you want to haul asphalt, you might need insulation.
Specing the truck can be tricky. For example, I've seen tandem dump trucks with 16K steers that weigh around 21,000 empty and can legally gross 50,000 giving you 14.5 tons of payload. I've also seen heavy spec trucks with 20k steers that weigh 24,500 empty and can legally gross 54,000, giving you roughly the same payload but you're dragging around another 2 tons all the time.
Same thing for trailers. We run short 22' trailers that can legally gross 72,000. With a tractor they weigh between 28,000 and 30,000 empty depending on steel or aluminum. That gives 21 - 22 tons of payload. The we have 32' 3 axle trailers that can gross 80,000 but they weigh around 31,500 empty, so you get about 24 tons. Some of the 40' frameless trailers are lighter at around 29,000 and can haul 25.5 tons legally. However, that's a long awkward trailer that is fairly delicate and precarious to dump.
Clear as mud?