Thinking of getting the remakes and 3.  How much better are the remakes compared to the PS2 versions?

Super Stardust HD

Excellent.

Now, while you don't actually need any PSN games as you have the greatest game of all time, the best ones to get are probably

WipEout HD (and fury)
flOwer
Super Stardust HD
PixelJunk Monsters

and that's probably enough for you to be getting on with

Thanks you good sir!! Yea its hard to turn down Uncharted 2 when it says "greatest game of all time" on the box. :)

Do you have to buy both Wipeout and Fury?

Flower & Siren

I don't have much other people haven't mentioned but...

Games that are amazing:  wipeoutHD, flower, braid, echochrome

Games that are great: crittercrunch, pixel junk shooter, pixel junk eden, trine, ratchet and clank quest for booty, fat princess

Games that were good: fl0w, zen pinball, Söldner X, Söldner X2

Games I didn't care for: rag doll kung fu, mushroom wars

Better frame rate and use of anti-aliasing are the biggies here...it actually looks better in-game than during the in-engine recorded cutscenes cause of this.

And part III is a masterpiece and a great technical showcase..

My PSN favourites so far are:

Supersonic Acrobatic Rocket-Powered Battle Cars

Joe Danger

Pixeljunk Shooter

Mushroom Wars

Burn Zombie Burn

edit: and Wipeout HD of course

I never quite understood all the hype for Flower by the way.

No, you can buy HD, then Fury is an add-on, which is about the size of the main game, which I must admit, I don't actually have myself

well, since almost every before me already mentioned Flower I'd say give Siren a try (if you're a horror fan)