I would not recommend an older flat screen, there is quite literally zero benefit for your described use case. Modern LCD/LED TVs provide much better image and features, and they can still be picked up for cheap.
Regardless, the TV won't matter much for any of the consoles you mentioned that have native HDMI output, with the quality of the panel being the deciding factor and not the console attached to it.
For anything without HDMI just use a scaler such as a RetroTink2x (or the also very capable knockoff Retroscaler2x from Aliexpress) so you can both improve the image quality for a modern TV and get the HDMI output.
Not all modern panels have 'smart' features, and those that do need not be used. Your use case is literally changing the source on the TV (smart or otherwise) to various HDMI inputs.
Older panels will offer worse image quality, be larger and heavier, likely consume more power (especially in the case of plasma TVs), and not have features that will improve gaming experience such as game mode to reduce input lag, upscaling to improve image quality especially for the X360/PS3 generation, and some sort motion-interpolation like Samsung's Game Motion Plus especially for 30fps games.
There is no benefit to getting older panels for your use case, except perhaps cost benefits although modern panels can still be found for very low prices. An older panel will not provide any sort of gaming advantage simply because it was manufactured around the time of a PS3 or whatever.