My Two Cents

When you're a stay at home dad, you are by definition a one income household. The experts say that ideally, in a two income household, you should be able to meet your bare bones expenses on one income in case one person loses their job. If you only have one income, you're playing a different game. You need a different method of filling the gap, you need an emergency fund. How much you need is up to much debate. The stability of your wife's job is a big factor. How likely is it that she's going to get canned or quit or have the company fall into a hole? If something happens is it likely that she's going to be able to find another job? If she has her arm chopped off in a horrible industrial accident, will you be able to find a job while she convalesces and learns to open jars with her teeth? There's no hard number that works for everyone, but at a minimum you should be able to meet emergency expenses. If your furnace goes out or you have a trip to the emergency room or you car disappears in the night, you should to be able to make it without sinking. Living paycheck to paycheck works, but it's stressful in the best of times. When the worst of times come, it's bad.
On that note, a budget is a good idea. You may or may not need to track every expense, but you should at the very least know for certain how much money comes in each week or month, and how much money goes out.  If you're a scientist, it's basic mass balance. You can't cheat a mass balance equation. If you need to save, make it a part of your budget, just like the house payment or groceries.
College funds and IRA's and investing strategies are all good things to think about, but if you have less than one years pay saved, you probably don't need to be thinking about following the market and day trading. The payoff at that level is just too small, controlling expenses is a much better use of your time and energy. For example, the general rule of thumb is that you can withdraw 4% of your retirement savings a year and have the savings last as long as you do. Quite a lot of leeway in that, but for an example it works. So, in order to save enough to pay $100 a month for cable, you need $1200 a year. If you work a little math, you see that you need to save $30,000 to pay for your cable in retirement. The average household income is around $46,000. The average household would have to save 2/3 of one years worth of income to pay for cable in retirement. I don't like cable that much. What this really shows is that it's often easier to keep control of expenses than to accumulate savings, especially when you're young and poor. 

Early Retirement Extreme is a wonderful site, especially the early posting. It should make you think about your relationship to money and spending. Really, the most useful thing you can do as a stay at home dad is not to screw things up. Don't spend too much. Don't buy things to make yourself feel better. If you don't feel manly taking care of babies, having a corvette sit in the driveway while you take care of babies probably won't make much difference. Being responsible and knowledgeable with the money that your wife makes shows respect for her effort. It's amazing how much that can be worth.
Just my two cents.