You don't NEED mylar to grow. Does it help? Yea, I'm sure it does. But, you can grow in a wooden cabinet just fine. You do get the reflective benefits of the mylar and probably make more efficient use of your lights if you have it.
I'd be more concerned about having enough lights. Personally, even for a small grow, I'd want at least 150 actualy watts. Which means about 6 of those 23w cfls. Don't now where you're located, but you can pick up a 6 pack of 23 w cfls at Lowe's or Home Depot for about 12 bucks. Grab a couple of those clamp lamps(about 7 bucks) and a couple of Y-splitters(a buck or 2 a piece) and take the reflector off the clamp light, screw in the splitter and then put 2 bulbs in each one. Also, you wanna keep em about 2 1/2 to 3 inches from the plant. Good Luck! What strain are you growing?