Hitman: Blood Money (No GA)

No need to play the previous, but blood money was an enjoyable game.

Blood Money was the first Hitman game I played. It's a good game on its own, I enjoyed it immensely, there was no need to play earlier game, but having played it certainly made me want more Hitman game :) .

If you really feel the need to learn the back story of Agent 47, look at getting Contracts.

It's like a revamped version of Codename 47 (Hitman 1) featuring that games best missions + new content (the mission in the arctic with the bomb was more like Splinter Cell, but still very good), with the bonus of the control system from Silent Assassin (which was less maddening) minus the annoying time-limited chloroform.

I played all hitman games so far and would recommend playing the old ones, too. Although the story isn't mind blowing, it has one and it's nice to see how the franchise evolved over the years :)

But that said: The first two games (Codename 47 and Silent Assasin) have a pretty brutal difficulty and especially the first game lacks the "perfect assasination"-gameplay and is thus far less enjoyable than the other parts.
If you like Blood Money - and I'm sure you will - I'd suggest to pick up Contracts - as it depicts the events of the first game, but with more satisfying gameplay.
Nevetherless Contracts is rather short,so you may not want to buy it at full price.

edit: too late D: