I'd leave a gap between turns if you are going to run full power. You'd
have to calculate the actual voltage across the coil on each band (which
EZNEC can model for you) then from that figure the voltage between
adjacent turns. That is the voltage that the insulation has to withstand.
Depending on how you wind the coil, you may be able to get by with
close-spaced turns, but that also increases the self-capacitance of the
coil. Spaced windings generally give a higher Q coil.
ON4AA's excellent coil calculator is available at:http://hamwaves.com/antennas/inductance.html
If you are going to wind the coil on a piece of PVC pipe, secure one end
temporarily then put the whole thing in the freezer for an hour or so.
The pipe shrinks more than the copper wire, so you can then work some
of the slack out of the wire and tighten it up. The wire will warm from
your hands, so give it a couple of tries. When you are done and the
coil is back up to room temperature, the wire will compress the pipe
slightly and the turns will be very hard to move.