In the end you'll need the adapter, a set of component male to component male video cable, the audio breakout box, a dual RCA male to RCA male cable for left and right sound, a SCART switch so you don't have to disconnect and reconnect to the adapter every time you want to use a different console, and a SCART to SCART cable to go from the switch to the adapter.
A lot of older consoles natively put out an RGB signal, which is far better than the next standard, composite. You just need the right cable, and those end in a SCART connector. There's a common SCART to YUV adapter for sale on eBay and Amazon for around $50 that will work. It takes the SCART cable and puts out YUV component video. I use it on my US SMS (looks amazing), US Genesis/Sega CD/32X, US SNES, and my Japanese Saturn with no issues.
You might be thinking of video problems converting 50Hz PAL video to the NTSC standard, which is shared between the US and Japan. As long as you're not dealing with old European consoles they should all be compatible.
Once everything is said and done, if you're going from composite video to this, it is worth every penny. If your systems are modded with s-video already it's debatable, but still an improvement.