> I was wondering how may, and what kind, of bass traps I would need for my control room. <
You could use an alternating mix of panel traps and mid/high absorbers, as shown in the forum FAQ article. My studio is similar in length to yours, though at 18 feet it's a bit wider. I have 17 wood panel traps and 11 mid/high absorbers, and it's pretty near perfect. So a dozen or so panel traps will not be too many for your space.
I plan to install some mid/high absorption near the peak in the ceiling to reduce the focusing effects that occurs when recording string sections. But if your ceiling is flat you won't need that additional treatment.