What's the best way of making money?

I was initially emphasizing the fonts of key aspects of each method, but there are too many, so instead I'll simply tell you what to look out for: source and cash per unit time. Source means stuff like which activity or diversion, the difficulty level if it's an activity, or the vehicle and location if it's a barn-storm. These methods are aside from buying as many properties as possible to earn money over time passively, aside from buying that money DLC, aside from completing the missions that have bigger cash rewards, and certain other things.

This video claims $10,000+ (e.g., $11,913) in three minutes with Professor Genki's Super Ethical Reality Climax. Let's be generous and round: 12K/3 = 4K/minute. My record, with a partner, for cash is $24,907, in medium SERC. Restart will take a little over 4 minutes and 20 seconds = 260 seconds. That's about $5,748 per minute ($95.8/s), at best. Deaths detract from time, for example.

This video claims $40-80K per minute at the air-port. The barn storm lasts from 2:03 to 2:07, earning $10,216. It restarts at 2:22. 22-3 = 19 seconds. $32261.0526/minute = $537.684211/second which is not as good as the title claims. Caveat: Their method is only available close to the end of the game because it requires a vehicle that you may not get, depending on your decision in the story.

This video shows flying a plane at the air-port. I can't run its numbers well because it speeds up the video for the return pass, but it earns $5,108 per pass and takes a while to make a return pass (longer than another method which earns more per pass, so calculation isn't bothered with).

This video shows flying a VTOL jet at the air-port. Starts at 0:17, earns $5,108 per pass, and returns to the start after two passes at 0:58. 58-17 = 41 seconds. $5,108*2/41 = $249.170732/second = $14950/minute.

This video shows camping Luchadores in an Apache helicopter. It earns respect at the same time as earning cash, but this easily earns lesser cash. Thus, I don't want to bother to crunch its numbers.

[Video demonstrating camping Professor Genki spawns]
Even if I do find such a video again, factoring in the time that it takes to find Professor Genki can be from minutes to hours. Hours? There's a video series on YouTube whose original premise is finding Professor Genki. It spans more than one video. Don't believe assertions that Professor Genki spawns at a specific location; he only spawns randomly anywhere.
Nevertheless, if the game throws you a golden bone and you stumble upon a Professor Genki respawn, spawn camping Professor Genki is hands-down the fastest way to make money at $300 000 per kill. Recommendation: 2/5, it's not a livelihood, more like a windfall.

Sad Panda Skyblazing can be glitched such that a roof-clearing bonus is repeatedly awarded. 0:46 enters, $408350, 3:30 exits. The cash amount is modestly projected. 3:30-0:46 = 164 seconds. $149396.341/minute, $2489.93902/second, which is over 7 times Arapice Island barn-storming. Downside: Requires DLC and reproducibility. One commenter commented that it requires two players. I just recently learned about this, so I haven't tested its reproducibility. Upside: May be the fastest way to earn cash and may be fun to do with two players.

Helicopter barn-storming Arapice Island: 0:13 to 0:49 is a complete pair of passes, starting and ending at the same point, with the same velocity. These time values are based on the YouTube player. 49-13 = 36 seconds. 2*$6,166 = $12,332. $20553/minute, $342.6/second, $1233200/hour, sustainably.
Other benefits: With this method, you can pop on a podcast, and take it easy while still being efficient. The Thompson is available as soon as you enter Steelport. Downside: It's easy to bump into the smoke-stacks accidentally.