It looks good. How much room do you have in there though? Can you raise the lights? You want to make sure to have a few inches from your lights to the plants. I posted some pics of the kind of fixtures I use. You have to wire these but they are easy to do. Lowe's sell fixtures that are a rectangle, with 3 sockets, and about 18" long. I haven't tried them but 2 other people have and they both liked them.
I'd recommend working on a new box to replace that one. Cardboard will work but it is unreliable. I think I would make a nice wood box with some size to it so you can get plants to a decent size, or you can do a SoG.
Until then you should definitely make the inside of your box white. I use white duct tape. I'm not sure how reflective it is compared to other things but it works. You can also get an emergency blanket from WalMart. It's only a few bucks and close to mylar. It just isn't smooth.
Also, you should try to have the exhaust coming out of the top with the intake at the bottom. That way cool fresh air comes in, up past the plants, over the lights, and out. It keeps the plants cool and takes heat straight from the light out of the box. Also, unless you live out in the middle of nowhere you will need a carbon filter. Plenty of DIY threads here. The smell can get ridiculous without one.
Just a few ideas that I thought might help. Let me know if you have any questions.