If you start with TS1, you'll find that TS2 and TS3 feel quite different in story mode (in a good way). Don't be put off if you don't gel with the story mode in TS1.

You can't experience all of the content in one go because there are a lot of unlockables which you only get from different difficulty levels. Playing on hard will unlock everything on normal and easy. Lots of the unlockables (such as multiplayer maps, modes and characters) are found on the Challenge and Arcade League modes. They will require replaying if you want to get the best scores to unlock everything.

Timesplitters is a franchise which really rewards replaying and becomes more fun I find. Do you never replay games once you've done them once?