This may help you http://www.ultrabookreview.com/1834-best-budget-ultrabooks/ keep in mind that for games, the new generation Intel graphics are not that bad especially for older stuff, but keep it to the i5 CPU, you should be able to get one in your budget.
If you want a small case/screen, Lenovo X260 is good, Lenovo Yoga 700, although the video cards in the Yoga is a bit weak since it's based on a low power CPU for heat/size/power saving.