You want a monitor that can pivot. Newegg has filters to search for pivoting monitors.
If you just want cheapest, here is a 18.5" 1366x768 for $115. http://www.bhphotovideo.com/bnh/controller/home?O=&sku=963999&Q=&is=REG&A=details
But 1080p isn't too expensive and this 21.5" is $150. http://www.newegg.com/Product/Product.aspx?Item=N82E16824009493