Install 4 cans about 36" from the walls for general lighting in a room that size.
If it's office space, install the cans directly over the work space.
Halo cans are inexpensive but over the years they have become really crappy. I use Elite brand now. They use a thicker gauge metal.
What I generally do is remove the existing switch box. A plastic nail on box is very easy to remove. Other types of boxes may present challanges.
You can change the box to a 2 gang and add a separate switch for the new cans or you can simply rewire and eliminate the switched portion of the 1/2 switched recep.
Either way, removing the sw box allows easy access into the wall cavity for your new cable.
Basically, your 2 cable will run from the switch to the first can, to the second, etc.
You will need to pull out the switch and describe or post pics of the box and the existing wiring to get accurate instruction. Wiring is done using many different techniques.