I don't know if you are missunderstanding it on purpose but I am not saying that Sony doesn't work well with the ps5 I am saying they make weird decisions with regards to VRR. I also tried to point out that have since added auto genre mode and auto HDR mode that controls settings between the tv and ps5 to calibrate the color based on content from the PS5. I am not talking about HDMI CEC which not Sony specific. You can read about it here:https://www.sony.ca/en/electronics/televisions/a90k-series/specifications#features

Sorry if I was unclear, Sony TVs are great with the PS5. They are a bit weird though since they control both hardware pieces. They had VRR support on the PS5 but not on their own TVs. They have since fixed it and their latest TV go into a PS5 mode that calibrates the colors for the PS5

Depends on your budget so I will keep it a bit more generic. I would say go for 4k resolution. HDR is sweet to have, but not a must. If you start looking and/or read reviews there is a lot of talk about higher refresh rate which is in my opinion not as important because a lot of the AAA games are at best running at 60 fps.

Brands: In general, LG and Sony are probably the best brands to go with in my opinion. LG has the best bang for buck and usually a slight edge on features. The downside is that they run their own OS so some apps might be harder to find. Sony on the other hand runs Android TV so it is easy to get all types of apps. As an example getting a VPN on a sony TV is the easiest thing ever since it is basically just downloading an android app. Sony only has the edge on calibration out of the box. The image processing is an edge for sony and you will spend less time having to setup the tv to get it to look good. The downside is that you are paying a premium for the Sony name. Sony also control the price meaning you will never find a deal on Sony hardware unless it comes from Sony corporate or it's a clearance sale.

TV type: When it comes to the type of TV, there is nothing that beats OLED and if you can afford it go for it. Otherwise there are different types of LED technologies that have their own advantages and disadvantages. The only reason you should stay away from an OLED is if your TV is in a room that has a lot of direct sunlight shining in and you tend to use it during the day.

Purchase of the TV: In terms of buying the TV itself there are recommendation to try and view them in real life. This is a bit tricky and keep in mind that all TVs have a retail demo real that is not always representative of how it will look in your home setting without the godawful fluorescent white that you have in stores. Good thing is to compare TVs in the same store setting. Absolute best thing is if you can see the TV in action at a friend. Lastly, get the TV delivered if it larger than 55 inches. Costco includes the delivery in the price so don't bother buying it in person unless there is warehouse only deal and even then think twice about delivery.

I would recommend to get the largest TV you can afford in your budget. Console games on a large TV in 4K is just amazing. I think it is worth splurging to get a good TV and go a bit above your initial budget because they are mature enough that you can stick with it for a solid 10 years. If you cheap out you might end up regretting it and be reminded about it every time you watch it.