I'm look for a tv or monitor (with the cable input for tv) for gaming

Size isn't a huge issue but I'd like at least 22in. I play mainly first person shooter games where input lag makes a huge difference in a gunfight. I'd like to not spend more than 250 but 200 would be more preferable. Having the cable input is important for TV in a dorm... thanks I hope this is the right subreddit.