Short answer: No. Long answer: It would be a better experience, as you understand more of the back story about where the zombies came from, the deal with the bees, why you are collecting statues of a reported (it's because he covered wars, you know.)and other tidbits. But it's not like Mass Effect (or assassins creed to an extent) where it's a direct continuation of the story. Different people in each game with a small cross over on some DLC.
But the other two are worth playing. And I am sure they could be had for cheap. You may want to start there as you might not enjoy the 1st ones as much after playing three. It won't be as bad as playing the 1st AC after playing the others, but they are more linear and confining.
The 1st was pretty unforgiving on time management. The people you try and rescue are total idiots (especially you Aaron. You can get stuck on the only zombie in a 5 mile radius). I don't think (havn't played in a while) that you get combo weapons until DR2. There are no weapons lockers, you had to find everything as you go, (but you can have a bigger inventory) and weapons are pretty flimsy unless you find the right books to extend their life (three books for bladed weapons, especially double chainsaws, and life gets easy). Though it does make the game interesting, because you are always exchanging out weapons. Keeps it from getting too boring by using the same katana for the entire game. You might find yourself with nothing but a frozen swordfish and a tub of cooking oil. But it's still fun.
I found DR3 to be a little overwhelming at first with the huge open world, as compared to the mall in 1. The mall was pretty straight forward and the stores where listed on the map. There was only a couple of things I didn't like about DR1. It was easy to miss things if you didn't budget your time. You miss out on a couple of pycho battles if you don't get to the location on time. The damn convicts in the middle park. They are driving a humvee with a .50 cal at a time when you probably havn't found many guns, and are a pain in the ass....and they ****ing come back several times after you kill them. The next day you are expecting a quick jaunt to the park as a short cut...nope! The Goddamn convicts and their Goddamn Humvee are back. WTF? And the worst of all? Otis. ****ing Otis.
This sums it up nicely: http://www.vgcats.com/comics/?strip_id=204 The guy calls you, and you can't hang up the phone and fight zombies and screws you all up.
But over all it was a fun game. I really enjoyed it. I'll give you the best advice ever though. Remember where the hell you came in the mall at. (Upstairs of the security room) Everyone forgets where the hell they came in, and when it comes time to un-ass the mall in a hurry, they are running around trying to find the exit until bad things happen.
DR 2 improved on the formula with combo weapons, a little more open area, and a few more things. But it also added money to buy things, and money isn't the easist thing to find. You need to find zombrex every 24 hours for your daughter, and buying it is a quick way, but it gets expensive fast. You can earn money for your SP game in multi player, but you need 3 other players to start a game, and it was hard finding players a few months after the game released. I bet it would be a real undertaking now.
So if you have a 360, I'd say get them before you play 3, but if not, you won't miss out on much story, just a lot of fun game play. --- Jesus Christ! what the ****'s blown up now? -Me after 6 months in Iraq