My vote is go with the HD retrovision cables:
Yeah, they're a bit on the pricey side, but they're a HUGE step up from the ps2toHdmi adaptors,
But if you already have the OEM component cable, you should be okay.
As long as you have a way to connect them to your display, you'll be getting the highest quality from your console.
As for getting that signal from the cables to your TV, there are various sealers in each price range, if your TV supports Compoent you could start with that,
If not, you could use a cheap converter (don't use cheap upscalers) like this: And you'll get a really clean image!
There are higher end scalers like the retrotink and ossc,
but if you want to keep the cost down, the retrovision+converter is really solid for the price!