How far apart do I space my recessed lights?

Sounds OK, I have a room that has a similar spacing. I would look at not using the bulbs that you are considering. Look at using compact fluorescent bulbs, (therefore you may be able to use a smaller fixture). You will lose the dimming part, but as a family room, it will probably see a lot of use and the lower cost and longer life of the CF lights will be well suited for that room.