You've counted -ati twice, this makes it five..
The differences are:
-flgrx : AMD's blob
-fglrx-envy : envy is a script that assists you in installing the most recent binary driver version. I guess this package is a newer version of the driver than -fglrx I'd stick with -flgrx anyway.
-ati : actually -ati just selects a fitting driver, -radeon in your case. -ati supports older ATI architectures (Mach, Rage, Rage128..) too.
-radeon : open source driver
-radeonhd : another open source implementation with a slightly different approach
Both the open source drivers should support your card. Which is better suited to your needs is hard to say, I'd guess -radeon because it is more mature. If you want 3D, better stick with -fglrx. To configure your screens graphically (assuming -fglrx), install the package fglrx-amdcccle and run amdcccle.
Hope this helped you.