You can get high power at any voltage. Power is the product of voltage multiplied by current.
So, you could get 10 watts by having 110 volts at 0.0909 amps or by using 12 volts at 0.833 amps.
The 12 volt option would be safer, of course.
The classic resistor in a coil shape would be made of Nichrome wire.
A coil that was going to dissipate 10 watts at 12 volts would have a resistance of 12 volts / 0.8333 amps or 14.4 ohms.
Nichrome wire is available in different thicknesses and the thicker wire has less resistance per foot than the thinner wire. There are wire tables on Internet where all this is available.
http://www.interfacebus.com/properties-of-nichrome-wire.html
For example if you did want to make the coil above and you wanted a coil that had 6 inches of wire in it, then you would want Nichrome wire that had a resistance of 28.8 ohms per foot.
This would be 37 AWG wire according to the table above.
Wire comes in a range of thicknesses, so you would get whatever was closest to this value and whatever you could buy locally.
Finding some of this wire may be a problem as it is expensive to buy a roll of it when you only need a few inches. You could try a local electrical repair store and ask nicely.
This wire does not solder easily so you have to clamp a connection to it or get some silver solder.