re: How much to put down on a home? (more than 20%?)

stick with the 20% down, but I would honestly suggest you look for a cheaper home. Where in Jersey are you looking? You don't want to get in a situation where you're house poor.

The goal should be that your monthly expenses + some amount of excess is less than what you will bring in. Don't get into a situation where you'll have to pull out of savings for any extraordinary expenses. Kids in Jersey are expensive, even with your wife watching them full time.