Which would be the best for someone who's new to the Thief series?

Thief 3 is the newer and better game imho. If you don't plan to play the whole series, I'd go for Thief 3, especially as the price is the same.

Thief 1 and 2 are considered the superior games, while Thief 3 suffers from the creative straightjacket that is the X-Box and lacks the large open ended levels of the T1+2.
Thief 3 will probably be a disappointment after T1+2 so play T3 first.

I love DeMignon but he is obviously on crack. 3 isn't bad but next to 1 and 2 (which should be played in that order) 3 sucks. :D

;-D I anticipated a controversy about this, hence the 'imho'. I really didn't like the later levels of Thief 1 for example. Design and story wise not my cup of tea and overall I found the game to be too long (maybe it wasn't and just felt like that, but anyway no good sign). Furthermore, Thief 3 has superior visuals (based on the Unreal engine I guess) and more freedom of movement (a bit sandbox like), where the former titles lead you sequentially through distinct levels - both a matter taste.

The Thief series is good and definitely worth it, so if heptarch plans to play them all, there's no question were to start. If he only wants to play one of them for now, I'm not so sure. Ex post I'd probably only play the last one.

Here are playthroughs of mission one of all three parts:
Thief 1 Mission 1: http://www.youtube.com/watch?v=BstW7EmR6rs
Thief 2 Mission 1: http://www.youtube.com/watch?v=DeZRBWCWWm4
Thief 3 Mission 1: http://www.youtube.com/watch?v=3KWCP9ZmNB8
(There's a lot of tutorial content in Thief 3's first mission, but I don't want to spoil anything by posting a later mission)

It's all good, and you do know I was just playing with you right? :D I mean, you are nuts, but I mean it as a compliment.

Sure ;-) I just wrote a few lines to elaborate my first statement a bit further for heptarch.

There's a storyline order, and the sequels do reference their predecessors. E.g. I imagine some of the things The Eye says in TDS might perplex someone who hadn't played T1.

If you're just interested in sampling Thief-style gameplay, The Dark Mod is free...

I think the "eye" period would confuse anyone who went to #2 before #1. I loved that story and normally I don't care about game stories.