There are dimmable fluroescent fixtures but you will need to go to an electrical supply or lighting showroom to obtain these. I don't believe the big box stores have anything like this. I would like to suggest that you may want to think about incorporating different types of lighting in your basement. The play area can have a fluorescent fixture. You may want to have incandescent lighting (lamps) for the TV and reading area. The future bar area should be worried about later as with a drop ceiling you can add lighting. Since I am not sure the depth that you have in your drop, you can check and see if you can get recessed fluorescent lights for the play area. Any reliable electrical or lighting showroom should be able to assist you with this. If not, you can always check the fluorescent lighting manufacturers on line to get the specifications of what is available. Try Lightolier, American Fluorescent or any of the like. The recessed fluorescent lighting that they are doing now is really quite nice. You can even get lenses that will cut the glare. For the different lenses you can check Malcolite. The only reason I suggest different types of lighting is that you are doing different tasks. Most people like to read by incandescent lighting and lamps really are the softest for this purpose. Also, in the TV area, you would want to be able to regulate the lighting so that there is no glare on the TV. If you want you can place a few recessed cans around the perimeter. Also, you can check out the fluorescent websites because they are doing extremely shallow fixtures that are surface mounted.

Recessed lighting cans will last very long and the smaller the aperture, the more expensive the material cost. The labor to install the cans will be larger cost component. If there is a cost concern, use the existing 6" can lights If you are intent on replacing the 6" cans with 4". About the same number as the 6" cans assuming that they provide sufficient light. The CR 4 and the baseline CR6 (Home Depot) Cree modules have ~ the same output. Cree modules work well (- good output, dimming performance) and come with an integrated trim ring.

Those cans make your ceiling the equivalent of Swiss cheese for sound isolation. I’d find the smallest LEDs you can, and use the fewest amount. Also invest in some rugs upstairs with a nice underlayment or pad. They really do help to dampen footfalls noise. You’d lose some height if you do a resilient channel or double your Sheetrock. Is this an actual rental unit? Or just a place for grandma and grandpa?

I had the same question a year ago when we finished our basement to be a gym and sitting area. I settled for a 72" grid ( 72" in each direction from the next light) with 60 watt equivalent LED bulbs. Since my length and width were more than 'x' number of 72" increments, I just divided the overage by 2, and that determined the starting point. IMO, the basement has good light for my use.