@Atom: Back in SC3k, my cities invariably went bankrupt after a few game months, just the same as you I was never able to balance my expenses and income.
What I do to keep my expenses and income balanced, is to not include certain things until I really need them, and try not to place them until I can afford them. As a personal rule, I try not to let my expenses be more than $1000 over income. Of course, you'll find what works best for you as you play.
When you just start, ask yourself what do you need the most. If you want any development, you need power. Without it, nobody will move in. So assign some small zones and build a windmill or two (they're cheap for low power reqs). As the city grows you'll need to add more windmills, but once you have 4 or 5, that's costing you about the same as a gas plant which produces a lot more power, so you should change over.
Then you need to take a look at your taxes. Higher taxes will discourage development, and lower taxes will encourage it. Think of which population/commercial/industrial types you want the most in your city, and adjust taxes accordingly. Normally (this is from the SC official guide, but actually it varies with the overall desirability of your city), taxes from about 12% upwards will make that population segment start to leave.
I don't like dirty industry, it's the least you want in your city as it decreases desirability for all other development types. Sometimes I let it in and then raise the taxes, and sometimes I just raise the taxes so they don't come at all. Also, the ordinance for clean air discourages dirty industry as well as encourages high-tech industry. Use it if you can afford it.
I usually don't add anything else for a little while. Then add a fire station, some time later a small hospital and later schools as needed, but only when income is above expense in about the amount I need for what I'm about to add. I usually don't need police until way later.
Always keep your power, health and educational funding just enough for their capacity to be just above actual use. Fire department funding just changes coverage area, so adjust it as needed. I don't like to change police funding, it doesn't significantly affect coverage but it does affect performance - and you will see that soon.
I could go on and on, but I better let you get used to all this I said before cramming more down your throat. Just let me know how do you do after this.
Edit: Wow, I didn't expect this post to be this long.