Seeing your high school graduate off to college may mean a welcome drop in your car insurance rates. Or it may mean you’re now frantically shopping for a car. Yes, some kids still travel around by bike. And some schools still bar freshmen from bringing their own wheels. But many students want or need cars to get to off-campus jobs, for example. And those who commute to class from home or off-campus housing often have no choice. According to the National Survey of Student Engagement, 27 percent of freshmen now commute to college by driving, while 57 percent of seniors use their cars to get to school.

But before making the rounds of dealerships, parents should cast a cold eye over their kids’ driving records, advises Anne McCartt, senior vice president for research at the Insurance Institute for Highway Safety. “Have they gotten tickets? Have they obeyed the rules?” Because of inexperience and a tendency to take risks, teenage drivers are four times more likely to get into an accident than older drivers.

[In Pictures: Best Cars for Students]

Assuming a car is deemed a good idea, three key traits to shop for are “big, boring, and slow,” McCartt says. The IIHS recommends midsize or large cars for new drivers because the bigger the “crumple zones,” the more crash energy can be dissipated before reaching occupants. But SUVs and pickups aren’t recommended, she cautions, as they weigh more and are taller than cars, which makes them tougher to stop and more prone to rolling over. As for boring and slow, “steer clear of sports cars,” McCartt says.

You’ll want to consider the crash test ratings and safety technology of any models you’re thinking of buying. Both the IIHS and the National Highway Traffic Safety Administration test cars’ ability to protect passengers by simulating front, side, and—in the case of IIHS—rear crashes involving cars of similar sizes. Both also estimate a car’s rollover risk and put cars through roof strength tests to assess how much protection they provide if a rollover occurs. There can be wide variation. The Dodge Caliber, which doesn’t have standard side airbags, gets a second-worst “marginal” rating in side-impact crash tests from IIHS while the similar-size Honda Civic, which costs less than the Caliber and does feature standard side airbags, gets a highest-possible “good.” Beyond top ratings, experts recommend insisting on side airbags, antilock brakes, and electronic stability control. ESC is an essential safety technology for inexperienced drivers, safety advocates say, because it minimizes the danger of going into skids; when the system detects a loss of steering control, it steps in and applies the brakes to individual wheels to help the driver regain control of the car.

With the exception of the two “cars to watch,” each model on the list that follows has four-star (out of five) or better crash test ratings from NHTSA and is an IIHS Top Safety Pick, a designation that means electronic stability control is a standard feature and the car earned the highest scores possible in IIHS crash tests. A couple of entrants are just making their way to the U.S. market, but have proven themselves in European crash tests. Also, each selection ranks in the top half of its class in the U.S. News automotive rankings, an indication that it’s popular with professional car reviewers. The fact that all of the vehicles featured start below $20,000 should make them popular with parents, too.

Best New Cars under $15,000

Kia Forte. Manufacturer’s Suggested Retail Price: $13,695
Kia is making a name for itself by building affordable cars that are loaded with standards. Available as a sedan, coupe, or new-for-2011 hatchback, the Forte comes with a long list of standard features that include traction control, electronic stability control, six airbags, and antilock brakes, as well as Bluetooth capability, a USB port, satellite radio, and a six-speaker stereo to grab young drivers. The Forte also has electronic brake force distribution, which varies the braking pressure applied to individual wheels based on the distribution of weight in the car. That helps the driver maintain control during panic stops. But what’s most impressive to car reviewers is the Forte’s crash test performance. It earned five stars from NHTSA for driver and front passenger protection in front-impact crash tests, as well as five stars for driver protection and four stars for rear passenger protection in side-impact crash tests.

Kia Soul. MSRP: $13,300
Students should like the Soul’s standout squared-off looks and standard four-speaker stereo with auxiliary input jack. Like the Forte, the Soul is a 2010 IIHS Top Safety Pick. And it, too, earned five out of five stars for driver and front passenger protection in front-impact crash tests, and five stars for driver protection and four stars for rear passenger protection in side-impact crashes. The Soul comes with standard electronic stability control, antilock brakes, electronic brake force distribution, and traction control, as well as front, side, and head curtain airbags.

Nissan Cube. MSRP: $13,990

The Nissan Cube has a unique rear window that appears to wrap around the side of the car, and a rhomboid design that means it has enough interior space for almost any college student’s gear. Buyers can choose unique interior options like shag carpeting. While most car reviewers complain that the Cube can feel a little sluggish while accelerating, parents may welcome a characteristic that encourages younger drivers to take their time. The Cube comes with six airbags, traction control, and stability control as standard features. It earns four-star rollover and front-impact crash test ratings, as well as five-star side-impact ratings from NHTSA.

Cars to Watch:

2011 Ford Fiesta. MSRP: $13,320
The new-generation Ford Fiesta debuted in the United States in July, after two years on the market in Europe. While it hasn’t been crash-tested here yet, it earned top marks for “adult occupant protection” in the European New Car Assessment Programme’s (NCAP) crash tests. For an affordable small car, the Fiesta comes with an impressive list of standard safety features, including antilock brakes, traction control, stability control, and seven airbags. For some extra cash, the Fiesta can be outfitted with Ford’s well-liked SYNC infotainment system. SYNC allows drivers to use voice commands to control stereo and phone functions. For 2011, SYNC will offer a “do not disturb” feature, which enables drivers to direct all incoming calls to voicemail and block all text messages while the car is moving.

2011 Chevrolet Cruze. MSRP: $16,995
The Cruze is another car making its way to the States after spending two years on the European market. Like the Fiesta, it has top crash test scores from NCAP, and its standard safety features include an exceptional (for its class) 10 airbags, antilock brakes, and stability control. For the kids, the Cruze comes with a standard six-speaker AM/FM/CD stereo with MP3 playback capability. Satellite radio is standard too. General Motors’ OnStar automatic crash response system, also standard, can detect a crash and contact emergency responders with the vehicle location even if the driver or passengers can’t.

Best New Cars for $15,000 to $20,000

Honda Civic. MSRP: $15,455
The Honda Civic, a popular small car since 1973, is bigger and safer than ever. A 2010 IIHS Top Safety Pick, the Civic also earned five-star crash test ratings from NHTSA for driver and front passenger protection in front-impact crash tests, as well as five stars for rear passenger protection in side-impact crash tests. The Civic earned four stars for driver protection in side-impact crash tests and a four-star rollover rating. The base DX model is sparse on everything but safety features: antilock brakes with electronic brake force distribution and front, side, and side-curtain airbags. For $750 more, the DX-VP model offers a 160-watt AM/FM/CD stereo with MP3 playback capability.

Scion xB. MSRP: $16,720
Students are apt to like the Scion xB’s cutting-edge sound system and custom options: They can choose their own gearshift knob and add individual touches like illuminated door sills and under-dash illumination. The car earned four-star front-impact crash test ratings, five-star side-impact ratings, and a four-star rollover rating from NHTSA. It also has a low starting price for a car with its interior space and safety features. There’s 21.7 cubic feet of cargo space behind the back seats, which is as much as some compact SUVs offer.

Subaru Impreza. MSRP: $17,495
For anybody heading north to school, the Impreza’s all-wheel drive, unusual in a car that starts under $18,000, may be a handy feature. The Impreza earns good marks from IIHS and NHTSA. However, parents may want to keep their kids from test-driving the WRX version, which is tuned for speed. Besides bumping up the price by $7,500, the WRX has almost 100 more horsepower than the base Impreza.

Volkswagen Golf. MSRP: $17,620
The Volkswagen Golf is a rarity in the affordable small-car class: It actually has a comfortable interior. It also has strong safety ratings from both IIHS and NHTSA. If you’re willing to spend $4,734 more, you can get a diesel engine that gets an estimated 30/42 miles per gallon city/highway. That should cut fuel costs and leave more money for . . . books.

Hyundai Sonata. MSRP: $19,195
The 2011 Hyundai Sonata has made quite a splash with its swoopy design and unusually low base price for a midsize car. Standard features include satellite radio, an auxiliary input jack, and a USB port with iPod interface. With Hyundai’s 10-year/100,000-mile powertrain warranty and the Sonata’s roomy interior (the Environmental Protection Agency actually classifies the Sonata as a large car based on its interior volume), this is one model that a new college student should be comfortable sticking with long after graduation.