First off: Cliffski, I'm so impressed with the quality and quantity of games you are able to produce by yourself. I didn't think it was possible to do anymore.
In my experience, the hardest part of the game is getting over the hump at the beginning. There is a VERY (too?) vicious feedback loop where if your ship starts to fall apart, it will both cost you money and inhibit you from making money and your crew will disappear because they don't want to work on a deathtrap. It seems that once you approach this situation, it's very hard to get away from it. The difference between occassional problems and constant breakdown is very minimal, so you want to prevent breakdown all together. As you stated, that's hard to do when you don't have a lot of money to begin with, but there's good news.
Breakdowns become more prevelants when you upgrade your ship, so only upgrade if you absolutely have to. It may be necessary to take some risks early on, but usually there's a planet within 10 LY of where you start, and you have a few thousand dollars to work with. Your first runs should only be between those planets, if it is at all possible. You don't want ANY breakdowns, so try to hire an engineer on one of those two planets. Make sure to buy a second crew bed if you don't have one before leaving the first planet, because the second planet may not have one for sale. If you have less than 2 passenger beds, try to get two if you can afford them, and the same with cargo holds (hazardous if at an industrial planet). However, controlling breakdowns is your first priority always. This takes a lot of risk out of the equation.
You don't want to have to hire any extra crew until you're financially more secure, which is why you want at least 2 passenger beds and 2 cargo bays before you even worry about anything else. Then judge your situation and decide what you want the ship to focus on. I usually go with hazardous materials because they have less risk than smuggling and time doesn't matter for them. They are quite lucrative, too. However, that doesn't help if you don't start near them. As soon as I can safely afford it, I'll get an extra couple pods for whatever I'm focusing on and an extra crew to deal with them, and another fuel pod for backup. Usually sticking between the starting couple planets is still okay, especially if the fee per ton for docking is low. Make enough money to get the auto-repair station before doing anything else. It saves you a TON of money in the long run. Once you have an engineer and an autorepair station, you almost can't lose.