Should i start playing Thief from the first game?

You'll miss quite a lot, including a great tutorial level, some excellent levels in churches and wilderness and will not understand why Garrett is in the situation he is in when playing Thief 2. Start from The Dark Project.

While I think Thief: Deadly Shadows (the third game) is awesome, there are a lot of references to the stuff in the first two games, and you should play them to understand.

I've only played the third one, and though I didn't feel lost in the story (as far as I know they're all mostly self-contained), I'm sure there must have been references to characters, locations, events, etc that I missed because I didn't play the others.

Any game or film should not require you to play/watch the previous ones to understand it - that's a sign of not being as well written as it should be. But in my opinion you will almost always get more from playing the series from the start.