Rtings is probably the best site to look at for finding a tv with high refresh and low latency
I couldnt find a tv under 500 for what you are asking. The best I can do is this: https://www.amazon.com/gp/product/B01E69WHP6?tag=rtings-tv-bm01a-20&ie=UTF8
55" that meets your criteria at $597
Snagged a PSTV For a steal at $25, but the memory is several times more expensive than the console. Im hoping with the holidays to snag a decent deal on 32gb or 64gb cards. Any help would be appreciated.