I can sympathize. I've been working on my setup for the last 5 or 6 years, but the majority of big improvements/additions to the pipeline have come in over the last 2 years or so since I decided to consolidate all of my consoles onto one TV. Unfortunately, that meant my massive Trinitron had to go. But don't worry folks, it has a new home in my garage, where it's hooked up to a PS2 with steel dance pads so I can play DDR to get some exercise.
Anyway, in my opinion, instead of buying an all-in-one clone system, the best way to play your old games on a more modern display is to use the original systems and convert their analog signals to digital via HDMI. While there are a variety of ways to do this, I have some solid advice based on my own experiences trying to get this all sorted myself.
First of all, avoid the cheap conversion boxes you see on Amazon and Aliexpress like the plague, and try to avoid stuff like Pound/Hyperkin HDMI conversion cables. Keep in mind that in most cases, the quality you get is the quality that you pay for.
Instead, I'll echo Bear78's sentiments and highly recommend one of the RetroTINK products, which are both very affordable and are available to fit a variety of use scenarios depending on your personal needs. The 2x Classic is the flagship RetroTINK product, but it's currently on its final run. It accepts composite, S-Video and component (YPbPr) inputs, and outputs a lagless 480p signal via HDMI. It can also passthru a pure 240p or 480i signal without line-doubling, and it also features an optional "smoothing" filter. It does not, however, support any input signal higher than 480i.
The 2x Classic is being discontinued because the 2x Pro and the 2x Pro Multiformat are essentially the same product with more features built in (like optional scanlines and different options for processing composite signals). The 2x Pro Multiformat is noteworthy in that it's the only RetroTINK product that can passthru 480p signals, but the tradeoff is that its picture quality is a little different than its brother's. Lastly, the 2x Mini is a scaled-down version of the 2x Classic at a lower price point which only supports composite and S-Video inputs.
Another popular product is the OSSC, which is a line multiplier like the RetroTINK, but can go much higher than a 2x scale. IIRC, it can go as high as 5x. It also can draw variable-width scanlines to convincingly replicate the "CRT" look if that's what you're into, and also allows you to finely tweak video options to best fit your preferences. A good friend of mine has used both the OSSC and the RetroTINK, and says he prefers the OSSC mainly because of its lag-free multiplication modes higher than 480p. He uses it on a 4k TV with great success.
However, the OSSC is also reported to be a finicky thing. Some displays may support some of the OSSC's multiplied outputs but not others, some displays may not work with it at all, and some displays just don't like certain video sources with off-spec timings. I can't verify how accurate any of this is, however, as I do not own one. Also noteworthy is that the OSSC has no input options available for composite or S-Video (instead offering VGA and SCART inputs), though some people have reported success daisy-chaining the RetroTINK 2x to the OSSC via an HDMI-to-VGA connector, using the 2x's passthru function to provide raw composite and S-Video signals for the OSSC to process.
Of course, it's important to note that regardless of the conversion option you go with, you are ALWAYS going to want to use the highest-quality input signal you can start with. For example, the best quality you can get out of an N64 (without RGB modding it) is S-Video, but an unmodded NES is stuck with composite as the best it can do. If your system supports YPbPr out, use it. If an HD Retrovision cable exists for it, use it. Or just use what you've got! In the end, if you're having fun and you're satisfied with the results, then that's the only thing that matters.
One last thing: if you do decide you want to hook up a bunch of systems at once, I highly recommend planning it all out first. For example, I went the route of drawing up a little schematic to use as a visual guide (as seen below, reflecting my current setup). If you don't have a lot to hook up (or don't want to), you probably won't need to go as in-depth as that. But if you ever plan to, it can certainly help.
