An antenna tuner will not make a big difference in reception with the various antennas described so far. One hint is the comment below about peaking the antenna tuner to increase the noise floor to find the sweet spot before transmitting. HF reception is governed by signal to noise ratio and the tuner will increase the signal some but will also increase the noise by the same amount. The end result on lower HF bands is little to no improvement in signal to noise.
For dipole type antennas, resonance has virtually no effect on antenna radiation but it does have an effect on feedline loss. If you feed a dipole with very low loss cable or balanced line, you can take say a 40m dipole that is perfectly tuned to 7.2MHz and add or subtract several feet of wire so it now resonates at 6.2 or 8.2MHz and there will be no change in reception or transmission. If there is its from additional feedline loss not due to "resonance" and this is the main reason for using TV twinlead, 450ohm ladder line or open wire line.
In my example above, as the antenna gets larger and approaches a full wavelength it will take on additional lobes and you will eventually notice a change in reception due to increased gain or loss in some directions due to the lobes and so on. By the way, the formulas mentioned below are backwards, 468/frequency is the total length for a half wave dipole and 234/frequency is for a quarter wavelength or one side of a dipole.
Some antenna like a very short loaded quarter wave whip (hamstick, etc) will exhibit lots of loss when not resonant due to the very high Q and there usually fed with 50ohm coax. Cut 6" off one of those and reception goes down the toilet fast, mostly due to increased coax loss. An antenna tuner will make a big difference in this case but its tuning the coax and antenna as a system.
The comment about receivers accepting a wide range of impedance is not true, its got roughly a 50 ohm input same as the transmitter.
One of the most useful things you can do to learn about antennas is find someone who knows how to "drive" EZNEC or similar antenna modeling programs. You can enter any kind of antenna with or without feedline and see exactly how the antenna will perform. You can then make changes in length, height above ground, choose various feedline lengths and impedance and see how it affects the antenna performance.
Antennas are very complex and most people treat them as very black and white, probably from simple experiences with CB antennas or listening to the "experts" discuss antennas on ch19. More often than not those experts are the furthest thing from the truth.
prcguy
Your right, an antenna tuner WILL help you on receive. The radio is going to work better receiving off a 50 ohm in feed. In fact, most guys with antenna tuners will use the noise floor or a received signal to begin tuning their antenna tuner. They will peak the received signal and then tune with the transmitter to finish tuning.
As far as 75 feet for 20 meters. That would be around a half wave if I remember right. The math is 234/f and f being the frequency in Mhz. of course then 468/f would be a quarter wave.
If you have a tuner, and I suggest using one, the best luck I have had is with a an off center fed dipole.
Some folks call it a Windom but that's not fully correct. A Windom works off a ground plane that is below it. An off center fed dipole is a simple dipole with the feed point moved.
I run an off center fed dipole cut at 80 meters. and it works wonders on 80 20 17 15 10 meters. for some reason I get alot of RF in the shack on 40 meters so I don't use it there.
Remember that an OCF dipole needs a 4:1 or 4 to 1 balun.
75 foot of wire is not going to be enough. But in true tight ass style I never went the way of the copper weld or other 'antenna' wire. Find a Tractor Supply or other farm store and buy a role of high tension fence wire. (Not barb wire although it would work, just a PAIN to work with) and use it. The zinc or galvanized works best and is really strong. I have had my wire antenna's in 8 MPH winds and not fail. Also, use the heavy plastic insulators. I have literally stood in the loop to pull tension into the antenna's (I'm 270 lbs) and never seen a failure at any point.
Also, these wire antenna's all but disappear once they are up becasue the wire is small. So for a stealth antenna it's also a good option.