One thing that should be added is that when the existing light(s) come down, there may be more wires in there than what is expected. Do not take anything apart that isn't connected to the lights. I've had many a housewife call me to come over when the husband was gone to work because he attempted to hang a new light and took too many wires apart, now nothing works. The last time, nothing worked except the light, but it wouldn't shut off. She told me he got it that far after tripping the breaker at least four times and called it good enough, he would fix it when he got home that night.
Whoever (it honestly wasn't me) wired my family room and dining room ran the travelers through the ceiling box. Both were also set up originally as ceiling fan with lights, the ******** used pancake boxes, then didn't keep the colors consistent. The other rooms have the 120 run to the ceiling box, a switch loop down, and all the receptacles fed off of it. It can get confusing, but if the only wires that get touched are connected to the light, all will be ok.