The amount of light should be determined by the use of the space. Unwelcoming (and unused) basements are usually dungeon-like (too dark). Use multiple switches or dimmers to can control how bright the room is. Another option is to use wall sconces.
Some considerations for you: The brain can easily detect small changes in pattern, so make sure that the floor joists above would allow you to have the lights evenly distributed according to your plan.
Halogen PAR 20 bulbs can be warm if you have low ceilings. Fortunately, affordable LED PAR 20 bulbs are readily available now.
It's better to put in enough lights than too few, and then regret it. Just do it right.
My basement is about 20'x24' and I have two switches controlling two banks of 12 pot lights (PAR 20 are 50 W bulbs) arranged in 3x4 grid. It took a bit of figuring to get the right spacing because of the ductwork, floor joists etc. The bank on the tv side has a dimmer. I am very happy with the level of lighting, and am gradually switching the bulbs over to LED as they need replacement. My ceiling is about 7' tall, so I don't get as much of a beam spread as you would with your 8' ceilings.
If you're concerned with heat or energy usage, use LED bulbs. If you do use LED bulbs, make sure your dimmer is compatible (not all dimmers are compatible with LED bulbs).
For your situation, I would recommend 12 pot lights in a 3 x 4 grid. If concerned about cost, an extra switch is cheaper than a dimmer, particularly if you are using LED bulbs.