I've browsed through this forum, and watched a few videos (including this one: https://www.youtube.com/watch?v=lHoOKLWIMKU) on getting older systems on HDMI. But still had a few lingering questions.

Here's what I'm currently working with:
Retron 3 (Composite and S-Video)
Wii (with it's standard Composite connector)
PS2 (with it's standard Composite connector)

My TV is a TCL 55UP120, 55" 4K - It has HDMI and RCA/Composite input

For now, I have the 3 systems going into an auto Composite switch

I've also currently running it through $20 Amazon RCA to HDMI upscaler (1080 or 720, set to 720)

I've tried a couple combinations, and here are my issues:
Running the Retron into the RCA ports on the TV (through the switch or not) the image is stretched. This TV offers Auto, Zoomed, Direct, and Stretch as options. Through the RCA ports, they all look stretched to different degrees. Direct looks the least stretched, but seems to be off the bottom of the screen. Auto (which I think is Stretch) puts everything on the screen, but... stretched. Still doesn't look good tho.

Running things through the HDMI upscaler looks the best, but the image still gets stretched.

Here's what I'm looking for:
NOT the best picture... I know it won't be perfect.
No modding of the systems.
Not stretched... I'd like to find a solution that pillarboxes the video

I'm looking to use a switch if possible, since this TV doesn't have a lot of free inputs.

It looks like a lot of the good scaling solutions (like the OSSC and Framemeister) are working with RGB/component. I'd be willing to get decent component cables for the Wii and PS2, but I'd still need to get that to HDMI. Could I get an S-Video to component for the Retron?

So, the tl;dr;
I'd like a solution that allows me to switch between the 3 systems, keeps the 4:3 ratio, and I'm looking for price over picture. OSSC may be an option price-wise, but would be at the top of my budget.