Try a game called Prey.......... you could pick this little gem up now for as little as £3/$5.
Prey has a decent story, tricky puzzles and insane physics (walking upside down ect) and it will keep you entertained.
As mentioned Orange Box is a great package, and again its cheap now so you can't go wrong.
Halo 3/Reach are another obvious choice......... and if you have friends around you can play up to 4 players on the same T.V. (i know you said "single player" but i thought i would throw that info in there anyway)
Also, seem as you are getting Modern warfare why not pick up Call of Duty 2 for 360, the reason i say this is because it's a completely different campaign to Call of Duty 2: Big Red One on PS2, XBOX1 and Gamecube.
Edit: Hell yeah............. Singularity is a fantastic FPS experience, the above posters are absolutely correct.
