All of the major brands you've heard of make a good laptop these days. Every user has specific things about that experience that they prioritize, so recommendations get complicated. The laptop that suits everyone costs a fortune, and the bargains all eschew something pivotal that people are looking for.
If you're a realist that knows what to expect from a sub-$1,500 notebook, then pretty much all of them will be suitable for you. We'd need to know a lot more about how you'd actually use it to be specific with recs that would be helpful for you.
For example, if the plan is to hook it up to a TV sometimes, what are the alternatives? Playing popular PC games with your laptop actually in your lap is almost always a horrible experience. They get hot and loud, the keyboard and mouse solutions are limited, bottom-facing cooling solutions are terrible and potentially hazardous to the lifespan of the unit, and so on. And the second you set it down at a tabletop, you're essentially replicating all the discomforts you mention about desktop gaming.
Also, how high is your personal video sensitivity? TV gaming is more likely to demand higher performance at higher resolutions, which can easily tax a $1,500 laptop.
Again, assuming you're comfortable with all of that, most new gaming laptops will be fine for you. In that price range there are plenty of options for a 3070 or equivalent, and a 3060 will do the job admirably for hundreds less if you can tolerate sub-max settings.
If the your gaming time will mostly be on a TV, don't be so quick to dismiss the idea of an actual PC. Low-profile options are plentiful these days, and of course an actual PC will perform better, cost less, and be far more upgradeable. If you can find a place to put it -- even if it requires that you get clever or innovative about it -- it's definitely the better option.
But yeah, if your solution really needs to be a laptop, they're all fine. If you just plug "3070 laptop" into Amazon and browse reviews (sort by newest reviews to weed out the possible fake reviews that typically come early), you'll get a good feel for what's what. Be realistic and smart. If you're really going to be on a TV most of the time, don't blow your budget on a high-refresh display or touchscreen. And it's not all GPU and CPU either. Design can be pretty crucial depending on your use. If you're actually going to have the chassis in your lap or resting on something that gives (pillow, bed, etc.), vent locations are a big deal.
Once you start to narrow down your options, plug the manufacturer and model into YouTube and watch some reviews where you can see and get more of a feel for actual performance.
Generally speaking, the lower your target price, the more you'll be looking at options from companies that are more known for components (Gigabyte, MSI, ASUS). All of those will have comparable, perfunctory hardware. Nothing special about the designs; their systems are more function than form. Of those the ASUS have the best reps. The companies more known for full system builds (Dell, Lenovo, HP, etc.) tend to charge more for design. Sometimes it's worth it if you need thinner, lighter options with superior cooling and a sturdier, more elegant build, but on a fixed budget that will of course come at the expense of components.
So if you're good with MSI, you can get a pretty reputable 3070 rig at around $1,200 to start. Something "fancier" in the same price range will only get you a 3060. You'll find the occasional 3080 or 3070Ti option at around $1,500, just be sure to be thorough in your review hunt. Every manufacturer has lemon builds with known issues from time to time.
For example,
this is a really nice option. Reputable manufacturer, a model line with a lot of fanfare, but lotsa folks are reporting hardware failure. Might be the exception, might be the rule. If you plan to use it a lot and are quick on the trigger (and patient enough) to pursue replacement while it's covered by Amazon and warranty replacement that could take weeks from the manufacturer thereafter, then it's a solid bargain worth the associated risk. It's still being stocked despite being about 2 years old -- is that because it sold great and the reorders kept it in production, or was it never popular because of the issues and they've been sitting in a warehouse somewhere that whole time? Who knows? Feels like a crap shoot, don't it?
Sorry for the novel, but it's a loaded question. Lots to consider.
TL;DR: Whichever Lenovo you're looking at is probably pretty great. I have a Flex 5 that I got for work cuz I vastly prefer touchscreens to touchpads. Love it. Nice, solid build, but not thin or light. Battery is decent. Mine isn't a gaming system, but the integrated Ryzen graphics performs surprisingly well. Far Cry 5 runs pretty perfectly at mid settings. No significant bloatware; included Lenovo update and support software isn't intrusive or resource-intensive. Very happy with the purchase ($720 two years ago).