240 volt will require half the current. That’s why you can use smaller wire. P = I*V rms. Your main will have a max current carrying capability. In most new homes that’s rated at 200 amps. The available slots only matter if you run out; it’s more about the total current you have available when everything is turned on.
You still need a gnd and return connection. so four wire romex, return and gnd connected at the box. Yes you can make it work with three wire but you need to check local code, or be willing to say "screw it". bad deal if your house has fire damage and the insurance company checks, they'll use any excuse not to pay.
The down side of 240 is that it takes two slots per breaker, one for each line. In my opinion, it's the way to go with the power you're pulling.
I'd hook the circuits in parallel as opposed to series, keeps the wire more manageable. The down side is that's 4 single slots.