The better way to estimate the number of lights required is by the considering the lumens per sq ft vs light output from the lamp.
eg - 165 sq ft @ 20 lumens = 3300 lumens total.
Considering a Cree CR4 @ 575 lumens (546 lumens ~95% if a dimmer is used)

Total 6 lights.

The CR4 itself is ~ $40 or so @ Home Depot. Trim ring already attached. Can be used in a Halo can (E26 base).

Look at all the lights (when turned on). The Cree lights seem to have the least glare and dimming ability.

Thank you so much. Attached is a new picture. The real living area is 130 ft.ò the rest of the area is really closet. The 165 number is based on ordering the floor tiles. Still a bit confused considering the lumens, would it be better to go with the LED series a little over 700 lumens per can and only use 4? Or use five of either the Cree or Juno or all ProSeries? How should they also be placed? Thinking about labor cost also. Thank you for all help and input.

A higher output light would seem like a good idea. In practice, maybe not depending on the light distribution, glare,...

Look at the lights in operation before making your choice and price out each choice- trim, lens,... Since lamps like the CR4 and Sylvania RT4 are complete units (excluding the housing), it's possible to try them out.

6" can lights are cheaper.

The Cree CR lights worked very well for many people.

The install price would be identical - cost of installing the recessed can housing, wiring. Price depends on where you live.

The actual placement of the lights depends on whatever is above the ceiling board. ~2.5' from the wall would work. Since this is a bedroom, the lighting requirement may be reduced to 15 lumens per ft and the overhead lighting may be supplemented by table lamps

Thank you very much. You helped me a lot. I bought all pro series. I really am so happy with the help received on garden web.

Today, Led lights plays a vital role in lighting system. LED is a semiconductor diode which emits the lights with the help of electric current.

Here is a link that might be useful: optical design