Most of my Sims start with no money and live off what they can harvest or collect. They start planting a lot of flowers right away - roses, bluebells, daisies, chrysanthemums. and lilies. These plants generate money when they bloom - not a lot at first, but it adds up. The Sim is always on his home lot before 4:30 AM so he's there when everything starts blooming at 5:00 AM. At about 7;00 AM they start to harvest and collect everything from around the neighborhood. Time capsules are sold without being opened. I also sell all treasure maps. Money from the sale of what they collect and harvest adds up pretty quickly.
They unlock the painting skill for free by working on murals in San Myshuno. They learn to play the guitar, violin, and piano at the Casbah Gallery. Sometimes they get small tips while they're practicing. They can also use the woodworking table to unlock the Handiness skill.
They mooch free drinks at bars. I've noticed that bartenders seem to always have at least one freebie available. A hungry Sim can also get free chips at a bar.
City posters and Snow Globes: I keep one for the collections and sell duplicates. City posters are free money and it feels kind of cheaty using them.
The first three weeks that a Sim is in the game can be difficult but they're pretty resilient. Almost every place that has bathrooms, free food, and drink also have Sims to socialize with as well as a stereo, television, or computer for fun.
I just discovered the yard sale table this past weekend.
I had a newly turned Fledgling Vampire learning how to cook because he got inspired and wanted to make a group meal, even though he couldn't eat any of it. I had him start with fruit salads and garden salads. At level 3 cooking, I let him start using a stove to make starter foods like Mac and cheese and grilled cheese sandwiches. He ended up with a lot of normal quality food that he couldn't eat himself so he had a yard sale. He stocked the table with the dishes that he had prepared and then he marked everything up 300%, which I figured no one would buy but I wanted to see what happened. He sold everything! He had 2 more yard sales after that because he wanted to learn to bake. The last yard sale earned him $5,000 from the sale of baked goods like bread sticks, fruit pies, cheesy bread, and carrot cakes. He now has several vampire customers who buy his food items and provide vampire training too!
