There are many different types of mortgage programs out there, but as a first-time home buyer, you should be aware of the three basics: adjustable rate, fixed rate and interest-only.
Adjustable rate mortgages (ARMs) are short-term mortgages that offer an interest rate that is fixed for a short period of time, usually between one to seven years. After that, the interest rate can adjust every year up or down, depending on the market. These are good for people who don't plan on living in their home very long and/or are looking for a lower interest rate and payment.
Fixed-rate mortgages are more traditional and offer a fixed interest rate (and thus a fixed monthly payment) for a longer period of time, usually 15 or 30 years, though they're available in 20 or 25 year terms. These are good for people who like a predictable payment and plan on living in their home for a long time.
Both fixed and adjustable rate mortgages can have an interest-only payment. What this means is that for a certain amount of time during the loan term, you're allowed to pay only enough to cover the interest portion of your payment. You can still pay principal when you wish, but don't have to if your budget is tight. There is a myth that with interest-only mortgages, you don't build equity. This is not necessarily true, since you can build equity through home appreciation. The benefit to interest-only mortgages is that you increase your cash flow by not paying principal.
Remember to ask your mortgage lender or mortgage banker lots of questions about which mortgage is right for you and your situation.