I'm not really sure you will be able to get a super good screen for your budget unfortunately, unless if you consider getting an external monitor..

15.6"
Acer
R7-571-53338G1T, i5-3337U + Intel HD4000+ (1920x1080 IPS; touch)@RM2999[2.4kg], 8GB, 1TB, W8
V7-582PG-74508G52k, i7-4500U + Nvidia GT750M + 24GB mSATA + 500GB HDD + (1920x1080 IPS; touch)@RM3399[2.2kg], 8GB, W8

Asus N550JV-CN077H, i7-4700HQ + Nvidia GT750M + (1920x1080; IPS matte)@RM3699[2.7kg], 4GB, 1TB, W8, backlit keyboard

Dell Inspiron 15R (Special Edition), i7-3612QM + AMD HD7730M + (1920x1080; anti-glare) + 32GB SSD + 1TB HDD(5400rpm)@RM3199, 8GB, backlit keyboard optional, W8
Lenovo Y510p, i7-4700MQ + Nvidia GT750M(GDDR5) + (1920x1080)@RM3099[2.7kg], 8GB, 1TB, W8, red backlit, swappable ODD, 120w psu, 2 yrs
*prices in RRP, negotiable
You might want to go and try out the Acer and Asus notebooks' IPS screen 1st and see whether they are good enough for you. Otherwise, you can actually just get a smaller notebook i.e. 14 incher for portability, and connect to a much better monitor for better color reproduction