You can print out an Azimuthal map based on your location from NS6T's site here:http://ns6t.net/azimuth/azimuth.html
Then you can overlay it with plots of the patterns from different antennas to see
what areas they cover and where they have nulls.
One important consideration is your operating interest - you likely would choose
different antennas for rag chewing on 40m or working DX on 15m, for example
(though there could be antennas that work well for both.) Sometimes the best
solution is multiple antennas, especially for multi-band operation.
I've used a lot of antennas over the years. Long wires tend to be more directional
off their ends, but can be useful when pointed in general areas (such as Europe
or VK/ZL). But performance drops when it is too long - I've had best results around
135' or so.
For working DX you want low angle radiation - that typically means getting the
antenna up in the air (ideally 1/2 wavelength or more) or using vertical polarization.
With a 40' support, for example, you likely will have better results working DX with
a horizontal antenna on 20m and higher frequencies, a vertical on 80m and 160m,
and the option to try both polarizations on 40m.
Center-fed doublets can be useful multi-band antennas, but performance drops off
on the higher bands when they are installed in an inverted vee configuration. The
steeper the slope of the wires, the more the impact. If you are primarily interested
in 80m and 40m, this probably isn't an issue, but if good performance on 15m and 10m
is important then you'll want to install it as flat as possible, or use a trap dipole instead
so only the center portion is used on the higher frequencies.
I've also had good results with large horizontal loops for multi-band operation, but that
will require more supports. And I've worked a lot of DX using a simple dipole or inverted
On the other hand, a vertical might not be such a bad choice: the local terrain might
not be as bad for propagation as you think.
So my suggestion is to try several different antennas. A simple vertical - even if it is
just some stray irrigation pipe or wire held up with a length of 2x4 - will give you a sense
of what you can expect from that polarization. A quarter wave on 20m is only 17' or so
(and you can shorten that if needed) so it isn't difficult to experiment. Keep your eyes
out for some inexpensive supports - a TV push-up mast should get you up over 30',
irrigation pipe can be spliced together, or you may find a neighbor with an old over-the-air
TV antenna on a tower that is no longer in use. Put a couple pulleys and halyards on the
top so you can change antennas without having to lower or climb it. For long antennas
you might need end supports high enough to let the hay trucks through underneath. Then
put up a couple antennas and see how they work. Remember, no antenna is permanent!
But if you want a single antenna that can serve a number of uses, consider a 40m Bobtail
Curtain. Instead of the standard center wire, feed it with open wire line in the middle
like a doublet. Face it broadside to your desired direction. At the base, arrange a switch
or jumper lead so that you can either feed the open wire line in the normal manner, or
short the two conductors and feed it against ground. Yes, it will require some sort of
impedance matching, and some autotuners might complain about matching a high
impedance load (depending on the exact dimensions.) For initial testing you can walk out
to the feedpoint and move a clip lead. But that gives you a multiband antenna with two
different sets of radiation patterns to experiment with.