I remember the first car I ever drove. An old, boxy 240 Volvo. It's wasn't pretty, but Volvo was known for safety so I felt like I was protected. Cars from the 80s didn't have fancy safety features like airbags and antilock brakes. With so many car safety features it can be difficult to find the safest car.
One thing to consider is the number of airbags in the car. Does it only have driver and front passenger bags? Does it have side airbags and seat curtains? Newer luxory cars typically have front airbags and a row of side airbags to protect you on side impact crashes. Keep in mind that not all airbags will deploy in a crash -- it depends on the type of car accident.
SUVs aren't necessarily safer than small cars. This is partly because SUV drivers tend to "feel safer", so they may drive with less caution, particularly in inclement weather. SUVs are also prone to flipping over when they lose stability. This is less likely in a car that has a lower center of gravity.
To find safe cars, you should look at government test ratings and safety crash ratings from organizations like Consumer Reports. These ratings show you how safe cars are for frontal and side impact crashes, plus a variety of other safety features.