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Fear Effect 2 (see my winning review)
Resident Evil (one of em anyway)
Final Fantasy 7 (need i say more)
seen as how you have a PS2 it's probably worth buying the updated PS2 versions (eg MGS2) but there are some unmissable classics out there for next to nothing :-)
However - If you are on a tight budget and want to play some really good games then go for the latest editions of things like Tony Hawks, Wipeout, Toca, Colin Mcrae, Tekken - All the Final Fantasy games are excellent and for platformers the Crash Bandiccot games are excellent. Crash 3 will provide better fun than Crash for PS2 as the gameplay is not really that much different but the loading times will be normal and you will be able to get it for under 20 quid.
Have fun.
Anyway, i bought FF9 the other day, very good, i recommend it, but there are loads of great games for the PS1, MGS, Resident Evil and so on.
Not sure about scrolling beat em ups though.