What you need to know
1. Half-wave monopole is best (wrap conductor around one end and you're there) with good noise characteristics.
2. Add one (dipole) or two (as radials) elements to braid to decrease noise floor in a high RFI / electrical noise environment.
3. Materials make no difference, coat hanger wire still reliably receives VHF signals.
You will get similar results on other frequencies between 100 and 1100 MHz, if you know the frequency you want to hear.
Use results here to construct an antenna for your preferences.
Importance of wavelength
A specific frequency has a corresponding radio wavelength. To get the wavelength in metres, divide 300 with the frequency in question. For instance, AIS is 162 MHZ, so the wavelength will be 300 divided by 162 = 1.85 metres. Calculations are the same for other frequencies.
Antenna types tested are for VHF and up, from broadcast radio to ADSB signals. Use info here to select an antenna for a quick and easy job, lowest noise (Half-wave with 2 radials) or a compromise for size vs performance (Quarter-wave with 2 radials).
Strong shortwave signals are possible to receive even with a rubber ducky. Weaker signals need larger antennas, but shortwave is an entirely different cup of tea.
Indoor location, antennas taped to floor-to-ceiling windows. If you live in a condo, need a college dorm antenna, or cannot erect an outdoor version, select from the following options. Indoor vs outdoor is a separate question, for reference, comparison at the end of this post.
Nooelec RTL stick, cheapest 20 feet / 6 metres RG-59 coax with no shielding, no noise reduction apart from metal removed from end of USB connector.
SDRSharp 18.104.22.1684 with the excellent Level Meter Plugin, this allows me to measure peak power easily. Same gain, cables and location for all antennas, only variable is antenna to ascertain comparative performance.
Signal: local airport info system, steady signal with the same recorded voice repeated over and over again. Antennas optimised / cut using the above formulas to get full, half and quarter-wave elements.
Distance to signal 2.7 nautical miles / 5 kilometres, no line of sight, signal path over electrically very noisy environment, called "city" in english.
Materials: best available used, 2.5 mm diameter house grounding wire as antenna material just to be on the safe side, not that it really matters: see material comparison below.
Antenna types tested
Monopole: receiving element connected to center conductor. Full, Half, Quarter and 1/8th wave tested.
Dipole: two elements connected, one to braid and one to center conductor. Half and Quarter Wave tested.
Two radials: one element to center conductor, two to braid, forming a Peace-sign / Mercedes symbol. Half and Quarter wave tested.
Rubber Duckies: common on handheld transmitters and scanners, Icom (FA-S280C, around 20 USD), Uniden (stock, around 11 USD) and Baofeng (upgraded stock from UV-5B, around 13 USD). Adaptors required to connect to BNC shown.
Discone: Skyscan V1300 with 12 feet / 4 metres 50 Ohm cable, around 60 GBP / 72 EUR / 95 USD.
Evaluating performance by received audio is subjective, printscreens are not. Received signal is on the left under red vertical line, this should be as high as possible. Yellow speckles and small waves are noise, lower or less visible is better.
The Full Picture
Please draw your own conclusions from the screenshots below, white is noise. Less white=better.
Antennas organised by peak signal, gives you an idea what to expect noise-wise.
Quater-wave dipole and half-wave monopole same length, dipole needs twice as much (two) electrical connections. The single greatest cause of electrical problems at sea is connectors, hence the monopole recommendation.
Monopole - stock is the supplied telescopic antenna that comes with the RTL stick.
Ducky refers to rubber duckies, separate comparison against a monopole below.
Full-wavelength antennas in any form will be a challenge to mount, as 1.8 metres for marine band (156-162 MHz), and 2.5 metres total length for airband (118-134 MHz).
Adding elements to braid
Adding one or two elements (same length of wire as receiving wire) to braid reduces noise pickup, resulting in better signal-to-noise ratio.
Common on transceivers, noise pickup is significant in an urban environment.
Compared to a simple half-wave antenna the performance difference is striking, the lower noise floor is evident side-by-side.
Indoor vs Outdoor
Here's a direct comparison with a discone:
1. Outdoor means antenna 1 metres from window. 10 dB increase visible means 100 times more signal received.
2. All antennas, especially discones, should be outdoors. The concept of an indoor discone is a heavy compromise, buying a 100-dollar antenna then placing it in the corner is pointless.
3. If you cannot have an outdoor antenna, add two radials and tape antenna to window. Lower noise floor than a discone, better signal-to-noise ratio.
Click on the image below to check they aren't the same, no difference whatsoever by ear.
Note that signal height is the same in relation to noise floor, same performance on-screen and by ear.