I'm hearing two questions, so I'll provide two answers.
Will missing earlier games limit your understanding of this one?
Skipping DX1 won't prevent you from understanding the core plotlines of DX3. In that respect I agree with others: you don't have to play DX1 or its sad, sad lesser sibling DX2 to play and understand its excellent prequel, DX3. It's not like some games (*ahem* Witcher 2 *ahem*) where you can play through the sequel but will be buried in an avalanche of unfamiliar names and plot points.
Would you advise me to play DX1 before DX3?
Yes, absolutely—if you have time and can look past the 2000-era graphics.
If you play DX1, I believe you'll have a deeper appreciation of DX3's plot, what's behind it, and the events it's setting up for the future. In other words, you'll be understanding a larger gaming universe rather than a stand-alone game.
As a long-time DX1 fan I really appreciate DX3's countless references to the original (characters, dialog, music, map design, even access codes!), and I have a better understanding of why things are happening and what they mean for the future.
Another option is to play DX3 and then, if you enjoy it, go back and play DX1 for the background. My concern with that: As awesome as DX1 was in 2000, and in many ways still is, DX3 is 11 years better technologically, and has also been designed to take into account DX1's quirks and failings. If I had played DX3 before DX1, DX1 would be much less fun and engaging. I'd be distracted by everything that DX3 improved on. And that would be a shame; I and many others consider DX1 one of the best games of all time (PC Gamer considers it the best).
So if you play DX1 first, you'll have have a fuller appreciation of many subtleties behind the DX3 story as you play. If that interests you, I'd take DX1 for a spin. But whichever way you roll, you're likely to have a great time with DX3.