I used to use 12 pound test Stren...Yes, switching to Trilene for a spinning reel will help because it is a softer line with less memory...
Here are a couple of other suggestions:
When you spool line on a spinning real, put it on so it comes off the spool in the same direction as it is giong on the reel...The easiest way is to drop the spool of line into a bucket of water so is spins as you remove it...
After loading the reel, put it in a pot of luke warm water for about 30 minutes this helps the line take a set to the reel...
Finally, when you go fishing, strip some line off and pull it behind the boat with nothing on the end of the line, let out 50-100 yards and drag it a few hundred yards through the water while moving slowly...This will take all the memory off the line and then you will have less backlashes...
Also, when you cast, use your index finger to stop the line and hold the line until the reel picks it up...If you don't to this, you will get a loop in the line that will pull too much line off the reel with your next cast and you have another backlash...