"I am looking for security/stability and a full time position."
I agree, nothing negative about the previous employer. My last job before this one was not the greatest but I said I was looking for full time work and they just nodded and moved on. If you don't make it a big deal neither will they
If you get nervous, practice saying it in front of a mirror, that's what I do before interviews, practice all the questions I think they can throw at me. At my current job the boss was amazed at how cool and calm I was in my interview