A few things to keep in mind: a 4ft^3 box would be about 19.5" on each side, and a 10ft^3 box would be about 25" on a side. Volume of a cube obviously increases exponentially... oddly enough, with the cube of the length of a side. (Odd how these things work out sometimes...)
A 4ft^3 box is definitely not small, and there are plenty of 18's that would be right at home in a sealed design of that size. I'd suggest, especially if this is your first run at building a subwoofer, that you make a sealed box. It's much simpler to design and construct a decent sounding sealed sub than it is to design and build any version of a vented design, and for a lot of reasons. I'd also go with two separate boxes, if for no other reason than it will be much easier to move when you're finished. If you want to run them together in series or in parallel, you can still make the appropriate connections at the terminals on the box, and you have the option of changing your mind for whatever reason. I'd also wire the dual coils on each driver in series, giving you a single 8Ohm driver... then you can run in parallel for 4 ohms if you want. Or power them independently at 8 each. And if you decide to power them in series, you have 16Ohms (not necessarily ideal, but at least you don't risk killing your amp with a 2Ohm load).
If Bassbox is suggesting 4ft^3, you can safely bend that number by 25-30% in either direction, remembering that altering the box volume nominally alters the F3 of the box proportional to the change in volume. It has other effects, like the final Q of the system, but since this is your first shot at this, I wouldn't worry too much about that. Your point about smaller boxes requiring more power is pretty much correct... because of the smaller air column inside the box, the driver experiences the sensation of "riding on a stiffer spring". As the driver moves, it either compresses or rarifies the air in the box... less air in a smaller box will compress or rarify faster, and thus exert a larger force on the cone of the driver. It takes more amplifier power to overcome this, but it's a rapidly diminishing return and because the box may be restricting the motion of the cone, you can run the risk of overheating the coil. I wouldn't call "likely", but it's mathematically possible.
A 4ft^3 box is definitely not small, and there are plenty of 18's that would be right at home in a sealed design of that size. I'd suggest, especially if this is your first run at building a subwoofer, that you make a sealed box. It's much simpler to design and construct a decent sounding sealed sub than it is to design and build any version of a vented design, and for a lot of reasons. I'd also go with two separate boxes, if for no other reason than it will be much easier to move when you're finished. If you want to run them together in series or in parallel, you can still make the appropriate connections at the terminals on the box, and you have the option of changing your mind for whatever reason. I'd also wire the dual coils on each driver in series, giving you a single 8Ohm driver... then you can run in parallel for 4 ohms if you want. Or power them independently at 8 each. And if you decide to power them in series, you have 16Ohms (not necessarily ideal, but at least you don't risk killing your amp with a 2Ohm load).
If Bassbox is suggesting 4ft^3, you can safely bend that number by 25-30% in either direction, remembering that altering the box volume nominally alters the F3 of the box proportional to the change in volume. It has other effects, like the final Q of the system, but since this is your first shot at this, I wouldn't worry too much about that. Your point about smaller boxes requiring more power is pretty much correct... because of the smaller air column inside the box, the driver experiences the sensation of "riding on a stiffer spring". As the driver moves, it either compresses or rarifies the air in the box... less air in a smaller box will compress or rarify faster, and thus exert a larger force on the cone of the driver. It takes more amplifier power to overcome this, but it's a rapidly diminishing return and because the box may be restricting the motion of the cone, you can run the risk of overheating the coil. I wouldn't call "likely", but it's mathematically possible.
