I won't give you exact name, but I would advise you to get AMVA monitor instead of TN or IPS. Modern VA monitors have actually pretty good response rate. At least it should not be a problem unless you are a professional player. And if you were - there are still good gaming VA monitors with low input lag. I just bought AMVA and played Serious Sam HD and also Warsow with bots and did not see any problems. Should be OK in CSGO, Team Fortress, Unreal Tournament. Maybe I would have problems in Quakeworld.
Why not TN? Well. the image quality is the worst and angles are also not that good. Common choice instead of TN is an IPS monitor.
Why not an IPS monitor than? Well. They look good on the shelves, but if you want to play dark games, watch darker movies or be in a dark room they really suck. Just check in google - "ips backlight bleeding". Not only black is really bad, but on the corners (or even more than that) you have a big light like somebody was glaring you with a flashlight through grey material. In games like Thief it is really hard to see, not to mention the ruined experience of atmosphere.
But of course if you don't care about dark stuff go get some IPS monitor.
AMVA:
+++ Best black on all modern LCD's
+++ Really good colors (better than IPS)
+++ Good contrast
+++ OK input lag for gaming (for non proffesional gamer -VA response times are in line with IPS)
---- Input lag not so good as in TN monitors
---- Viewing angles are good, but VA panels have black crush and gamma shifting
=== You can buy pricey gaming VA monitor with low input lag
IPS:
+++ Colors better than TN (pretty good)
+++ OK input lag for gaming (for non proffesional gamer -IPS response times are in line with VA)
---- Input lag not so good as in TN monitors
---- IPS panels have backlight bleeding - horrible black
=== You can buy pricey gaming VA monitor with low input lag
https://hardforum.com/threads/best-reviewed-a-mva-monitor-thread-read-the-1st-post.1803228/ - opinions about some specific models
Jut be aware that Iiyama X2483HSU-B1 and Iiyama X2483HSU-B2 are actually different:
http://www.iiyama.com/gl_en/products/prolite-x2483hsu-1/
http://www.iiyama.com/gb_en/products/prolite-x2483hsu-b2/
The monitor I bought is Iiyama X2483HSU-B2 and it has gamma shifting while I move head :) I still prefer it to my LG IPS237L-BN I bought in April 2013.
I can finally play Thief now without light in corners :)