TN = fastest response times and cheapest price possible, but also worse viewing angles, if off angle on a TN screen you get colour shift.
IPS = better viewing angles, off angle on modern ips screens tends to show contrast shift (IPS 5 or so years ago didnt have this affect some kind of cost cutting has happened I think), better colour accuracy than TN, IPS weaknes can be poor blacks, due to backlight bleed. IPS is what I buy.
VA = viewing angles somewhere in between TN and IPS and contrast shift off angle, best contrast out of the three due to deeper blacks. VA is not very common now and got squeezed out when IPS moved into the budget pricing space. Modern IPS tends to be similar to VA for viewing angle characteristics.
For nvidia some screens have gsync, this will remove problems that you can get when the framerate is below the refresh rate of the monitor, so normally in that situation you get tearing if vsync is off or stutter if vsync is on, gsync you get neither but has a very big price premium.
Freesync = amd version of gsync and has almost no price premium as its based on a open standard, but nvidia have chosen to not support freesync presumably to maximise revenues from gsync.
Unless you feel you need gsync, then I would just go for the cheapest IPS you can find that is in the size/resolution you want and has a displayport.
My dell 2209WA screen was a older type of IPS and was the first cheap IPS on the market, off angle there is no colour shift or contrast shift and is an amazing screen, it sold very well but dell oddly took it off the market quickly, I suspect because the screen was deemed too good quality for the price point, since then all IPS I have seen are not as good as that IPS but still definitely better than TN.
AMOLED is deemed as the saviour but I have some bad news, it seems AMOLED is not immune to cost cutting reducing quality, my S3 and S5 phones with AMOLED screens had brilliant viewing angles like my dell 2209WA, but my new S7 phone the AMOLED on that has definite shift off angle, so something has changed on the newest AMOLED screens that I consider lower quality. However it is still superior to IPS phones I have used.