That seems like a nice TV (better be for that kinda money!)... new model, I guess; i've seen some older Samsung LCDs, pretty nice. You seem to understand that without a real HDTV signal hitting it, that unit is going to yield results that may disappoint, except for XVGA or component signals. So congratulations- you are now overqualified to be an A/V installs engineer.

Finally found list of PS2 specs: seems it'll output composite (sending that to a high-end LCD is casting pearls before swine... your non-HD TV signal [composite]probably looks better than it would on a plasma [which often looks worse than on a CRT when displaying composite video- very unforgiving and weak blacks], but probably still very sad compared to HDTV), S-Video (better but not much), or component (sweet!).
First bit of advice I'd give is to definitely use the component inputs on the TV for your PS no matter what else you do... that's about as good as it gets with analog... essentially the same type of signal that comes thru an analog VGA port. Sucks that the PS2 component cable is terminated with RCAs, but not too bad, although you may need RCA-to-BNC adaptors to connect to the TV (??) If so, that's worse, as there will be about 1dB loss for every connection in a video circuit. might be noticeable, might not.
Since you've already spent a lot of money, you might consider replacing that cable with three premade BNC-to RCAs... but I'll wager that at the PS end, it's some kind of funky proprietary head (probably only one). No big deal, just not perfect. But if the PS2 has BNCs, use them... with good cables (mid-range quality is fine; super-expensive video jumpers are a waste of money).
And other than refresh rate, I forgot to mention progressive scan- that should be enabled, if available... on the PS2, and the TV. That usually just makes it look "a liitle better", but sometimes without it you get weird anomalies.
Good luck!!