First, some good reading on the subject is W4RNL's
article on 5/8 wave antennas:http://www.cebik.com/58.html
Personally, I'd put up the 1/4 wave antenna and see how
it does, mostly because it is a lot simpler mechanically
to construct and mount. (Or build one of each and
compare them.) You can always use the same tubing for
the top section of the 5/8 wave antenna if you want to
try it later.
Matching shouldn't be a problem. With just a few
radials on the quarter wave antenna, the added loss
resistance will increase the input impedance. This is
why a quarter wave antenna often gives a very good
match to 50 ohms. Of course, with plenty of radials
(and the resulting lower losses and higher efficiency)
the SWR may be over 1.5 : 1.
You can just ignore an SWR this low, or you can add a
simple coil or capacitor at the base of the antenna to
reduce it even further. I'd start by connecting a 470
pf capacitor from the antenna to ground, then lengthing
the antenna a bit (perhaps close to 30'??) until the
SWR dips at the operating frequency. Try different
values of capacitance: at the 1 watt level, the old
mica "postage stamp" capacitors are quite adequate.
The other approach is to use add a coil from the antenna
to ground (perhaps around 0.5uH) and shorten the whip
to adjust the SWR. Neither makes an appreciable change
in the radiated signal: there might be an advantage to
using the coil since it would provide a DC ground at the
feedpoint, and you can make it out of a scrap of wire.
The 5/8 wave whip is commonly matched by adding a coil
in series with the feedpoint of about 50 ohms reactance
at the operating frequency (in this case 0.7uH or so.)
But I think you will have better luck connecting a coil
of about the same size between the antenna and ground,
then tapping the coax center conductor up onto the coil
at the point of minimum SWR. If you start with a coil
that is too large and tap it for both the antenna and
the coax, then adjusting the two taps alternately should
give you an SWR as low as you want.