You shouldn't necessarily avoid a CVT, but Nissan's CVTs are pretty bad (unreliable and unrefined).
For Corollas, look only at the 2014s and newer. Don't get the L trim; get at least the LE, which is the best value. You get many nice features with the 2014 Corolla LE, such as auto climate control, a touchscreen radio with bluetooth, and a backup camera. I rented a 2015 Corolla LE Premium and it was pretty good, although the CVT can rev the engine pretty loud. It was a Top Safety Pick, but only got a marginal rating on the small overlap crash test. I like this car more than the 2012-2015 Civics, but not as much as the Mazda 3.
As for the Civics, Honda cheaped out on the 2012 model (it was horrible) and did a quick redesign for 2013 that made it a better. Look for a 2014 or 2015 Honda Civic. It's reliable, fuel-efficient, and relatively comfortable. 2013 had a traditional automatic and 2014 had a CVT, which for Honda, has been reliable to this day. The CVT is hated by car enthusiasts, but most consumers like it because it improves MPG a lot. If you don't care about MPGs that much, get a 2013 Civic. It you do, get a 2014 or 2015. It was also a top safety pick.
Stay away from the new Nissan Sentras. They are so behind the Corollas and Civics I just mentioned. Reliability and owner satisfaction are at the bottom of the pack. The only thing it has going for it is a large backseat. It was NOT a top safety pick. It got a poor rating on the small overlap crash test.
The one I would buy in this segment is the Mazda 3. It's fun to drive, more driver-engaging, and good-looking. Look at a 2014 or newer. Drawback include a lot of road noise and the interior can be a little cramped. The infotainment system is finicky, too. It was also a top safety pick. When driving it, it feels smaller than it is.