Low lag matters the most
Put image quality on the back burner. First and foremost, you should focus on buying a TV with low input latency -- that is, one that minimizes the delay between output from your console and action taking place onscreen. High input lag won't matter much for a puzzle or strategy title, but it can sour a fighting game or a first-person shooter, where a fraction of a second can make all the difference. That's particularly true now that many sets support 4K resolution and high dynamic range (HDR), both of which can affect your performance in ways that you might not notice if you're only watching Netflix.
You're typically looking for a TV with input lag under 30ms at your desired resolution and color range while using a set's game mode, which disables some image processing in the name of performance. That's easy to achieve if you intend to play at 1080p or with HDR turned off, but beware: Some sets have unusually high lag when you invoke 4K, HDR or both, making them less than ideal if you own a 4K HDR-ready console like the PlayStation 4 Pro or Xbox One X. Most LG, Samsung and TCL sets performed well across the board as of this writing, but performance was decidedly mixed for brands like Sony and Vizio -- some are fine, but others bog down the moment you start playing in HDR.
Don't expect manufacturers to publish these figures, however. Remember how we said that TV makers emphasize video, not games? Instead, you'll want to turn to a third-party site like RTings or DisplayLag. They conduct thorough lag tests and frequently offer side-by-side comparisons that help you gauge the performance relative to competing models.
OLED versus LCD? It depends.
Now that OLED TVs are relatively affordable, they're tempting options if you can afford to splurge on a higher-end TV with gaming in mind. But should you? That depends on how and what you play.
OLED looks nicer as a general rule. It doesn't need back or edge lighting like an LCD, so you'll see true blacks instead of dark grays. Accordingly, it's your display tech of choice if you play in a dimly lit basement or thrive on creepy horror titles -- you do want that monster to surprise you when it jumps out of the shadows, after all. Also, the hardware-induced motion blur you sometimes see with LCDs is virtually nonexistent with OLED. While that's not always a good thing (it can exaggerate the stuttering in low-frame-rate content), it's great for preserving details in action-packed games. OLED can also be better for local multiplayer experiences like fighters and party games, since there's virtually no color shifting or reduced brightness at wide viewing angles, as you sometimes see with LCDs.
Don't run out to buy an OLED screen just yet, though. The technology can be prone to burn-in, which is when the display retains image elements if they stay onscreen for too long. While fears of burn-in are somewhat exaggerated with modern OLEDs (they're more resistant to burn-in and frequently include preventive measures like pixel shifting), you do have to watch out for it in a way you don't with LCDs. Do you regularly play strategy games where the onscreen graphics rarely change, or leave your games idling for long periods? You might want to skip OLED for now. It's better for action titles, not to mention gamers who rarely leave a TV unattended.
There are a few other areas where LCDs can claim an edge, and we don't just mean the historically lower prices. The TVs with the lowest lag and highest brightness still tend to use LCD panels. While OLEDs are quickly catching up (LG's 2017 OLEDs had much faster response times than their 2016 ancestors, for example), you'll likely want an LCD if you either insist on the lowest lag possible or play in a very sunny room. And then there's the simple matter of size. OLED sets still tend to be large, living-room-oriented models, while there are plenty of small LCDs well-suited to gaming in your bedroom or dorm.
It's generally wise to future-proof your TV regardless of how you use it, but that's particularly true with gaming. The console market frequently pushes the limits of TV tech, and it's becoming difficult to predict. Who could have anticipated the PS4 Pro or Xbox One X in 2013? You're likely committing to ownership for several years or more, and you don't want to buy a TV that's obsolete soon after you take it out of the box.
Ironically, 4K and HDR support are the easy parts. The odds are that any new gaming-ready TV you buy will support at least 4K, and likely HDR as well. TCL in particular has developed a reputation for making affordable game-ready 4K TVs. Don't worry about looking for 4K if you're opting for a smaller set, however. Most TVs under 40 inches don't support it, and you likely wouldn't notice the higher resolution at that size.
Rather, you'll want to think about features that require a deeper dive into the spec sheets. While you don't need to worry about refresh rates beyond 60Hz (your games aren't likely to need anything higher), you may want broader HDR support if you can get it. The PS4 Pro and Xbox One X both rely on the HDR10 standard for their enhanced visuals, but Dolby Vision support (present on sets from brands like LG, TCL and Vizio) may be helpful if future consoles or firmware updates take advantage of it.
And don't forget connectivity. You'll want as many HDMI 2.0 ports as you can get (some vendors may only include one), and preferably more ports than you need right away. Multi-console households are increasingly commonplace -- you shouldn't need to swap cables or buy an HDMI switch just because there's a new must-have system on the block. You may also want to consider a TV with Bluetooth audio, for that matter. While you might be happy to listen to speakers right now, wireless headphones could come in handy if you ever want to play while someone is sleeping. And don't forget to consider other factors. You're ideally buying a TV that can adapt to your life, and that means thinking about where, when and how you might play in the years ahead.