A camera mounted mic is the worst option since it is too far away to have the direct sound be the dominant source. Getting the mic close solves a lot of problems that a distant microphone creates. The wireless is a good solution worn by the speaker since the ratio of direct sound to ambient noise, reflected sound, and wind noise is a lot better.
All these video mics have the same electret elements that cost about $0.75. Since they are omni by nature, any directionality such as the cardioid pattern, figure eight, hyper-cardioid polar patterns are created by baffling, cancellation or damping all of which lower sensitivity. . Quality mics are not needed for this task at hand, There are much more expensive than the ones videographers are buying and you don't need them either. A lapel style mic that plugs into a smartphone is fine for moderate to short duration recording but the bandwidth is intentionally limited by the phone in the attempt to reduce noise and that might be what works best for this application. They would be no more than $10-15. Full wireless systems can be had for $40, including transmitter, mic and receive.Units designed for more stressful treatment like on stage by Shure or others are several hundred dollars. I designed my own UHF transmitters and receivers and had 3,000 made in China 15 years ago to used as a tour guide audio system and other than a few lost over the years, none have broken or needed extensive repairs. Whenever I needed a video sound recording, I have used those with very good results. When I had them made there was very little on the market that was less than $300 but now there are so many low-cost wireless systems the price has bee driven down on the lower end products. Here is a page on Amazon to give an idea of how cheap the simple systems are and probably the perfect solution for you:
https://www.amazon.com/Best-Sellers...nes-Systems/zgbs/musical-instruments/11974711
If you have any audio or recording questions just ask. I was a recording engineer and producer for 25 years and owned one of the most productive recording studios in the world, recording top artists ranging from Stevie Wonder, Metallica, Whitney Houston, Heart, Fleetwood Mac, Journey, Santana, John Fogerty, Aretha Franklin and many more, totaling near 200 gold and platinum records.