Trust me, Zams, the last thing you want to do with recessed lighting is space them evenly around the room, or run them consistently around the perimeter. My wonderful brother did this to my sister's house and it was like living underneath a runway! Get too many of them in the ceiling and it's like being under an incubator.
What you want to do is analyze your lighting needs at the floor level. For example, is there a place where you're going to have a seating area? You may wish to place a couple of recessed lights over the sofa/chair areas for reading (even if you also intend to use table lamps).
Will there be art on the walls? You may wish to place lights in the ceilings within about 6 feet of the wall as a "washer" -- this is a type of recessed light that is aimed at the art on the wall with an "eyeball" and gently washes light over it.
Is there some type of entertainment unit, or bar situation, in the room? Do you need lighting above the counters? Is there a hallway or passthrough area that will need a floor wash so that people don't trip over things? Etcetera, etcetera, etcetera... I'm sure you get the idea.
Decide where things are going to go, AND THEN you need to decide what type of recessed lights you need in those locations. Do you want to use the larger recessed lights, or the smaller ones (the smaller ones are slightly more expensive, but much less noticable in the ceiling). Do you care if you can see the face of the lightbulb? If so, you'll want to buy the type of recessed light that has a baffle deep enough to hide the bulb. And, do you want that baffle to be black or white (which is entirely personal preference)?
Now that you know what you want and where you want it, you should consider how many of these lights are in each "zone" of lighting. Do you want to be able, for example, to turn on the lighting over the seating area separately from the lighting designated for the wall art? Do you want to be able to turn on lighting for one portion of the room, but not another? Each of these zones needs to run to a separate switch. And, depending on how many lights are in a zone, it may determine how many circuits you'll need to use in the panel box. You may not be able to run every single light off of one breaker.
Go to the home center, or a good lighting store, and check out the options. Oh, and one more thing, make sure you put everything on dimmers. You'll be very glad to have that control.