Antenna and Coax Length

I have a question for this august body.

I found a link on the 1-26 associations web site talking about the
proper length of an antenna for operation at 123.3Mhz. This turns out
to be;

1/4 wave Length: 0.61 m or 23.95 in
3/4 wave Length: 1.82 m or 71.84 in

I was curious about the length of the coax. I was under the
impression that to get the maximum power out of the antenna, that the
combined total length of the coax *AND* the antenna needs to be taken
into consideration and needs to be an even number of wavelengths.
That prevents power from reflecting at the tip of the antenna and then
back into the trasceiver. This can not only rob radiated power but
might also damage the transceiver. A VSWR meter is used to tune this
for maximum radiated power typically by adjusting the length of the
antenna.

I may be all wet on this subject as I am an electronics engineer (a
bit pusher) and not an RF electrical engineer. Any comments?