This answer will be US-centric but hopefully most of the information will be applicable to other jurisdictions:
- Listen to those Credit Score commercials; just don't actually use their services. They are required to provide your credit report for free, without enrollment in any credit monitoring service. Get a copy and look it over carefully; look for anything that may be wrong, and work with the reporting agencies to get it removed. You want to go into the pre-approval process with the best possible credit score you can get.
- Don't buy more home than you can afford, even if you think you'll need the extra space of a bigger home. The less expensive the home, the less you'll pay in monthly mortgage. You'll be surprised how many kids you can stuff into two bedrooms while maintaining relative comfort.
- In this housing market, if you can't get a mortgage without any points, you're either not looking hard enough or you probably shouldn't be looking. A "point" is 1% of the principal payout of the loan, paid up front to the lender, usually in return for a break on the interest rate. Sounds good, and it can be worth it if by paying a point you get a 1% deduction in interest rate (you're basically pre-paying at 1% for one year, to get a reduction for the other 29), but if you have good credit you shouldn't need to accept points to get a really good rate (prime mortgage rates are in the high 2% to low 3% right now). If you can't get a mortgage with no points attached, get a copy of your credit report and credit score and make sure there aren't any major problems.
- Try to bring the full 20% of the purchase price to closing as a down payment; bring more if you can. While options exist, at least in the U.S., for homebuyers to bring as little as 3.5% to closing, all of them are "less now, more later" options that will increase your monthly payments, at least for a while, in the form of higher rates on secondary loans, and/or MIP payments on FHA loans.
- A 30-year term will lower your monthly payments, but increase your total cost of capital; not only will the rate be higher, you'll be paying it on more money longer. If you feel comfortable with 15-year terms, seriously consider it. At the very least, if you get 30-year terms, make extra principal payments as you can afford them.
- Some banks will allow you to make biweekly payments, each payment being half your normal monthly payment. This does two things; first, you're making 26 half-payments per year, equating to making 13 monthly payments which is an extra principal payment per year. Second, if the lender applies the half-payment when it comes in as if it were a normal payment (calculating interest as of the payment date, paying that, and applying the rest to the principal; this is a big if in the U.S. as they generally do not have to), then for the next two weeks you're saving the interest that would have accrued on the principal portion of the previous payment. If you're paid bi-weekly, this can help normalize your discretionary income from check to check as well, but this is usually a relatively minor concern if you have a buffer (6 months' expenses is recommended, but even 1 or 2 months' worth will smooth out these bumps).
- Understand that in the U.S., for the mortgage interest deduction to be worth it to you, it must, when added to other itemizable deductions, end up being substantially more than your standard deduction. You get personal exemptions for everyone in the house who isn't claiming themselves no matter which way you go on deductions, but you also get your standard deduction and your spouse's, which you give up if you itemize. The magic number for an MFJ return in 2012 was $11,900; if your total expenses for mortgage interest, MIP, property taxes, state and local income taxes (or sales tax), and charitable contributions were less than that number, and you didn't have any other big-ticket expenses (like having a kid; insurance doesn't pay everything and everything you have to pay out of pocket is deductible), then you don't really get a tax benefit from owning a home. The upshot is to consider this aspect when deciding how much home to buy; you either want the deductible portions of your payment to substantially lower your taxes, or you want to reduce those charges as much as you possibly can because they're not helping you on the Schedule A.