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Human Revolution is a prequel to the first Deus Ex so you won't miss out on any preceding storyline by playing HR first. However, HR is built on the same concepts (sneaking, finding alternate routes, talking your way out of problems) as the original and you might feel a little behind the curve since you're picking up the game concepts for the first time. And yes, you may miss some inside jokes about crawling around in ventilation ducts (it happens a lot in the first game, and a lot in HR as well).

Although I haven't finished HR yet, I expect it will tie into the events of Deus Ex (already there are some references to the future of nano-augmentation, a heavy plot point in the original) but you shouldn't miss out on these things, they'll just make sense when you play the original later on.

As for Invisible War, it takes place even later after the events of the original so you won't be missing out on any plot points there. In all honesty, some people don't really consider IW to be a proper sequel as it dropped or reduced a number of features that many people enjoyed from the original (most of which are back in HR). So don't feel bad if you don't play it, ever.

Depends on what you throw, but...yes.