Of the "near" repeaters, I can hit most or all of them with a 5w HT and a rubber-duck, though some are marginal. A 1/4 wave ground plane would be enough of an improvement to be worthwhile, even better if it's at a reasonable height.
In that case it won't take much of an antenna (or much height) to get the marginal ones as well.
Height makes more difference than antenna gain, especially when starting at low heights. Just a
ground plane on a mast above the edge of the roof may be sufficient to hit most of the repeaters
on low power.
Given the results with the HT, I'm trying to see to it that I'm at a net gain in signal strength by putting an antenna on the tower and losing signal in the coax (~150' worth) vs the corner of the house and 20' worth of feedline loss (LMR400 is the low end I'm considering, with LDF4 1/2" heliax most likely, though still a bit underrated for UHF)
The relative height of the two antennas will determine how much improvement you get.
You can compare coax losses using VK1OD's handy calculator here:http://vk1od.net/calc/tl/tllc.php
... I'm tempted to mount a second modest beam horizontally on the other side of the cross boom both to balance it out and to provide a SSB antenna. I think I'd reverse the direction of the SSB antenna so it would point "S" when the rotor indicates "N" as another attempt to keep the two antennas out of each other's near fields.
Actually a horizontal yagi should be mounted directly to the mast - a horizontal cross-boom
of conductive material will interfere with the pattern.
I suspect that a reasonably small colinear on top of the mast with a horizontal yagi below it will
do just about everything you want, unless you have multi-path to some of the local repeaters
(which a beam might or might not solve, depending on the relative directions of arrival of the
But you really will have to experiment and find out what works best in your specific situation -
we can't predict it from a distance. I generally suggest that folks build some cheap and simple
antennas like a ground plane and perhaps a WA5VJB "cheap yagi" to try out different placements
and heights. Based on the information you gather, you can choose a more permanent solution.