Online games to get:
Call of Duty: Modern Warfare 2 (COD 6) £40 - A must.
Gears of War 2 £15 - Play the original first, lots of people still play this online.
Halo 3 £10 - Fantastic Multiplayer, highly reccomended.
Fifa 10 £20 - Love the online and manager mode.
Left 4 Dead 2 £30 - All my mates say its a right laugh, I played the first one and that impressed me.
Single players to get:
The Orange Box 5 GAMES IN 1 (Half Life2, HL2:Ep1, HL2:Ep2, Team Fortress 2 and Portal) £10 - All the games included are brilliant, Half Life 2 is worth £10 on its own easily.
Bioshock £10 - Up there with the best RPG's I've ever played. (Fable, FF:7, HL2 are the best I've played and this isn't that far off)
Assasins Creed 2 £30 - Also been highly reccomended and has got high ratings on IGN, Gamerspot...etc.
Oblivion/Fallout 3 £20 - Both obviously are similar as they are made by the same company but everyone seems to love these game, however I do not.
Forza 3 £30 - Best racing game on the 360.
GTA4 £15 - Didn't really meet expectations but its still GTA...you can still blow up people and shit haha.
G.R.A.W 2 £10 - I really enjoyed this game. No one really plays online but like you said, your not to fussed about that.