I think you should first ask yourself what your communications objectives are. Are you talking about QRP for DX or QRP for local or interstate work?
When you know the answer to the above you can then move forward with antenna selection.
Factors you should consider are
1. Ground conductivity
2. The takeoff angle
3. Antenna and its associated losses with or without the matching network.
Hams have endless anal debates about this piece of low height wire and the other piece of low height wire. Most horizontal antennas have adequate radiation efficiency and at most a poor design with a poor feedline system has no more than 6 db loss. Now if you talking talking down the road or into the next state your major losses will come from either:
1. Ground losses
2. Takeoff angle loss or gain
3. Matching network losses
All things been equal its hardly even worth talking about this horizontal wire versus that horizontal wire if its close down low to the ground. Unless you can get it
up higher your performance is automatically limited. Dont ask other hams for signal reports. They all have useless uncalibrated S_meters and they will in a convincing
voice tell you that there useless S_meter tell them that your Super duper wire will have 10db over a G5RV. If you have any antenna that has 10 db over another similar antenna you either comparing it to a dummy load or you have something wrong. Most hams cant measure the difference between an horizontal antenna that 50% radiation efficiency and one that has a 90 % radiation efficiency. If there is a difference it mostly comes from a change in takeoff angle for the propagation at the moment or there is a change from vertical to horizontal polarization.
So getting back to your question.
If its just for local interstate use ANY horizontal antenna will most have very good efficiency. The best is simply a doublet or dipole at whatever height you can get it.
If you cant get the horizontal polarized antenna above 30ft you are not going to have much of a a DX antenna. I know people will tell you that they worked DX with the dipole laying on the ground last month, but last month and their location wont be your month, your location and your sunspot number or propagation conditions. Once you hit the 50ft height market horizontal antennas of any kind start to wakeup and perform well for both DX and local work.
If you chasing DX and you not located in a dessert the best portable antennas are undoubtedly a vertical polarized antenna. Now we not talking about a miracle whip or a ham stick clamped to the park bench. A real vertical with at least 2 radials or a vertical dipole. A good second alternative is a magnetic loop. Having a low takeoff angle even with the associated ground loss of using a poor 2 radial ground system is worth at least 10 db on a long haul path. Now if you have good conductivity you may pick up an extra 3 to 5 db without having to lay out many radials. On 40 meters the best portable dx antenna is a full size quarter wave wire on a fiberglass pole with 1 or 2 radials.
When you running 10 watts of power output you really have to pay attention to the efficiency of your system and in particular taking advantage of things like optimising take off angle gain. You see endless debates on various ham forums that go for 20 pages long and when you model the 2 talked about antennas you find one antenna with an efficiency of 75% and the other with maybe an efficiency of 90%. The gain difference at a particular angle is about the same because most hams cant measure the difference. Yet the thing that will give you 10db of gain, that is the takeoff angle is hardly mentioned.
All my portable antennas are optimized for the intended use. If I am talking to my friend down the road with country borders I dont give a hoot about what antenna I use. They all work even the ones with design and problematic feed systems like end fed wires and dipoles. Yes, everything works. I dont own any shop bought mickey mouse antennas that fold up into my wallet! Wire, wire and wire for local and NVIS work. For DX work its all vertically polarized antenna no other antenna is as convenient and delivers as much punch as a decent vertical antenna with a couple of radials. With my manpack radio and 20 watts I can have decent DX QSO's without screaming my lungs out. Normally I set up both a horizontal wire and vertical antenna. If the vertical becomes noisy because of QRM, I listen on the wire for improved signal to noise ratio. No, I dont have delusions about secret antenna designs that let me hear and work signals that are in the noise from a portable setup. All the stations that I work have decent antennas and I dont expect to work another QRP station on a DX circuit running a miracle whip and 5 watts. I take a dose of physics reality salts and look at my YC156 before I go portable to remind myself I should not have QRP delusions of grandeur. You cant pack K3LR into your portable suitcase!
So its very simple.
Height for might with horizontal antennas.
NVIS horizontal antennas or higher for local stuff, any antenna will do. Its pure crap talking about one horizontal piece of wire having massive gains over another.
Vertical polarised antennas for DX work and takeoff angle gain.
Use open wire line on everything if you going to use a tuner.
Avoid any coax fed antenna design that uses a tuner on multibands.
If you only want one good antenna make that a doublet fed with open wire line.
If you want loud signal the cheapest and most effective investment is a amplifier.
The best QRP power level is 20 watts!
This recipe is old hat and nothing new to most hams. Its just we get into these anal debates about everything that amounts to nothing and forget the very basics thats
60 years old. No need to reinvent the wheel and no need to argue or pretend that your G5RV or favorite wire into is a stack of 4 yagis on a 200 ft tower. Many hams are dreamers about the efficiency of their antennas. The differences in the real world amount to nothing.
I have a discussion going in the Antenna forum about QRO solutions for my home situation. It has been a confusing ride so far, with more opinions than there are types of antennas, but I am thankful for the suggestions I've been getting. I think it's going to take some time to work that out before I spend any money.
In the mean time, I realized today that I should start off where the KX3 is comfortable, with QRP. Rather than agonize over permanent antennas for now, I think it would be wise to begin my journey by learning about some wire antennas. I have some trees in my yard I can use. They aren't super tall though, the tallest being 15-20ft or so. I'm not opposed to getting some kind of mast either if my trees aren't going to cut it.
Kind of funny.. I've been so confused about what I was going to setup for QRO at home, I didn't bother getting the built-in ATU option for my KX3. I figured I'd be buying a tuner anyway. Well, I went ahead and ordered the option from Elecraft today....
My question to you QRP masters is, where do you think I should start? I'm interested in learning to make my own wire antennas, but I also wouldn't mind buying a high quality one, if I can't make one as good or better myself.
Thanks in advance for your suggestions! ~ 73's