By RACHEL LOUISE ENSIGN

This New Year's, you may want to make a resolution to go house hunting.

Home prices are finally starting to recover, but they're still low enough to get a great deal. Add to that interest rates that are at historic lows, and 2013 may be the time for first-time home buyers to finally get in the game.

"We think the answer, definitively, is that home prices have bottomed," says Stan Humphries, chief economist of real-estate firm Zillow. "Right now, buying looks very attractive, even for short-term time horizons."

While the timing may be right, the tougher standards lenders imposed after the housing crash are still very much in place. So buyers with good credit and a hefty down payment may benefit the most.

"Now it's all about the rules," says Jeff Conn, a mortgage banker in the Atlanta area.

Window of Opportunity

A bevy of data suggest housing prices have finally begun to climb back. So there's a window of opportunity before prices start a faster upward march.

The median price of an existing single-family home was $178,700 in October, up 11% from a year earlier, according to the National Association of Realtors. But that's still down 13% from $204,800 in October 2007.

Buyers can find particularly good deals in the Phoenix area, where home values are rising steadily, but are still more than 40% below the peak, says Mr. Humphries. Home values have also started rebounding from their bottoms in the Dallas, Miami and Denver metropolitan areas, but are still below their peaks—meaning there are potential deals to be had, he says.

Prices are on the way up, but mortgage rates remain in the bargain bin. The average rate on a standard 30-year fixed-rate mortgage hit a record low 3.46% for the week ended Nov. 16, according to data provider HSH.com. The average rate on a standard 15-year, fixed-rate mortgage hit a low of 2.84%. And rates are expected to stay low next year and further out, thanks, in part, to the Federal Reserve's moves to keep interest rates low until mid-2015.

For first-time home buyers, it may be easier to buy. Many first-time buyers are opting for loans backed by the Federal Housing Administration, since they now have looser credit and down-payment criteria compared with the tougher criteria for standard loans. The typical rate on a 30-year fixed-rate mortgage backed by the FHA was 3.31% last week, according to HSH.com.

But the FHA is now facing billions of dollars of losses on loans originated between 2007 and 2009. To help bolster its finances, the agency recently announced a series of measures including higher annual insurance premiums and a change to rules that allowed insurance premiums to lapse. Typical borrowers have to pay an up-front insurance premium of 1.75% of the loan amount and, starting in 2013, a higher annual premium of 1.35% of the balance, up from 1.25%, says Keith Gumbinger, vice president at HSH.com.

Many potential buyers have sat out of the market and rented instead—because they were waiting for prices to bottom out, found it to be a cheaper option or couldn't qualify for a mortgage. But the jump in renters after the housing collapse led to higher rents throughout much of the country. In many cases, it no longer makes financial sense to rent instead of buy.

In about three out of four U.S. housing markets, it now takes less than three years of owning a home with a standard 30-year mortgage for buying to be cheaper than renting a similar space, says Zillow's Mr. Humphries.

Tougher Standards

While home prices are trying to inch back to pre-crash levels, lenders are not returning to the lax lending standards of the boom market, when loans with no down payments were not rare, says Mike Fratantoni, vice president of research at the Mortgage Bankers Association.

It's still back to basics. That means "good credit, a down payment, and document, document, document," says Matt Vernon, head of home loans sales at Bank of America . "Credit [was] always available, but it's different. Not different than it was a decade ago, but different than it was five years ago."

Borrowers will typically need a FICO credit score of at least 740, and a minimum 20% down payment to qualify for the best rates on a standard mortgage, says Mr. Gumbinger. FHA-backed loans require a minimum 3.5% down payment and lenders often require a minimum FICO score of 620, he adds.

And be prepared to break out the paperwork—lots of it. You'll typically need to have one or two years of tax returns, as well as pay stubs from an employer, which some lenders didn't ask for before the crash. Also expect to provide statements from your bank and brokerage accounts, says Mr. Vernon.

"There's got to be a clear paper trail," says Mr. Conn.

Also, some mortgage pre-approvals are expiring faster, in some cases lasting only 30 days, compared with 60 to 90 days before the bust, says Mr. Gumbinger. After that, you'll need to show the lender updated financials.

"We tell people to never leave any stone unturned," he says.