Introducing new person into kids lives

I starting casually seeing someone, and after a month, my sons insisted I introduce him to them because they felt they needed to "check him out" and make sure he was good enough for me. We've been seeing each other for several months now, still nothing serious, cause I'm not ready for that, and he sees my younger DS every so often; if he comes over to watch movies or football, he always brings pizza and sodas for both of us and is sweet to my son, but moving in? No way. Since we work nights, there have been plenty of times he'll come hang out after work and we end up passing out, which my younger DS thinks is hysterical, and my older DS thinks is sweet, cause we're "old" and can't stay awake long enough to watch a movie after work. I'm not sure how they'd feel if it were serious, but I suspect they would be fine, so long as the guy wasn't a jerk. But, my ex and I were separated for over a year before the divorce, and my boys encouraged me to start dating, mostly because I think they were afraid I'd let my ex come back again if I didn't find someone I liked better. They even picked out my date outfit. It's very weird, but as long as they are ok, I guess we'll figure it out.