NOT A GOOGLE CHROMEBOOK. At most 14" and 1/2" thick when closed. I'm looking for something light-weight and something that won't break down in a month.
Chromebooks are like phones, all you can do is use google and everything that includes google. Nothing else. I'm sorry if that's not the way you see it but nothing is gonna change my mind about Google Chromebooks. Not a fan of Chromebooks either. Look for sales on Lenovos and Acers. Sometimes you can get one for just under $300. It's the long weekend so you might pick up a real bargain. Don't pick anything up with less than 4 gigs Ram. It'll be a waste of time.
However, if you want small and thin, you will have to pay more than $300. That's not going to happen at your budget. $300 will barely buy *a* laptop, yet alone one that thin. Anything in that price range is going to be the cheapest, slowest, oldest hardware that the manufacturer could scrounge together.