12.5" - 13.3" laptops are typically both ultra-portable and relatively powerful so these type of laptops generally start at around $850.
11.3" are in the realm of netbooks and they are generally in your price range. Here are two options:
Dell Inspiron 11 = $350
- Haswell generation Celeron 2955U - Lower power consumption for longer battery life.
- Touchscreen
- Windows 8
- Only 2GB of RAM, but can be upgraded to 4GB (only one RAM slot)
http://www.newegg.com/Product/Product.aspx?Item=N82E16834300146
Acer Aspire V5-131-2629 = $320
- Slightly older Ivy Bridge generation Celeron 1007U CPU (not as power efficient as Haswell generation, but still good)
- No Touchscreen
- Windows 7
- 4GB of RAM...