It’s not guaranteed you’re going to end up with that mission, so keep trying until you get it, but story missions in general do afford a better wad of cash than the more lowbrow multiplayer activities, so it’s a steady means of acquiring dollars. Unfortunately this method will break the continuity of your story completion, but if you’re happy to side-step that, simply hit Left on the D-Pad, head to Quick Join and then ‘Story Mission On-Call’ to be dropped into a posse.
This is a great lump-sum that will set you up nicely at the start of the game, especially if you’re working towards getting a good rifle for hunting or upgrading your camp.
It’s a tough one, but it nets you something in the ballpark of $200-250 for first-time completion, similar to the heist payouts in GTA Online. One of the story missions currently available in Red Dead Online is titled “Kill Them, Each And Every One,” and it involves you and your squad storming Fort Mercer with helmets on your noggins. This is by far and away the easiest method of making quick money, though it comes with a catch.