When I think of government cyborg-assassins (and when you read manga you will think about that eventually), I generally don't think of teenage girls. If I do, I expect the manga to have the serious undertone, but with the overtly slap-stick humor of R.O.D. Or perhaps something like Trigun, darkly serious at times and ridiculous the rest of the time.
If that is what you want, Gunslinger Girl is not for you. Gunslinger Girl is dark. It starts by focusing on Henrietta, a girl who gets taken by the government's Social Welfare Agency after she survives an attack that kills her family and leaves her missing limbs. Supposedly, the agency helps handicapped youths. But in reality, they take hurt young girls like Henrietta, make them cyborgs, brainwash them to forget their pasts, and then pair them with handlers who train them to be assassins. Henrietta and her handler have a brother and sister relationship, but their job means they are always in danger and political plays in the government keep threatening to abuse or shut down the project. The story evolves slowly, but small hints at larger developments are dropped to keep you reading.
What really sets Gunslinger Girl apart, though, is the artwork. With some manga, you can read the words and skim the pictures, but in Gunslinger Girl you need to study the pictures to see what's going on. The story is told more through art than the dialogue. A character says one thing, but the depicted setting and character's facial expressions reveal to you what they are really thinking. Everyone lies--even to themselves--and the artwork gives away who is lying. It's a more nuanced approach than most manga take, but it works with chilling effect, and it's where Gunslinger Girl gets its dark feel from. If that's what you like reading, jump in with both feet and enjoy while the secrets are revealed.