I'm pretty sure you'll be fine. If you're really familiar with the way Halo: CE plays, you might be taken off-guard by a few changes (you can hijack enemy vehicles, for instance), but Bungie used a lot of forward-thinking to design Reach very much in the vein of the original game.  
 
It'll probably be a bigger culture shock going from the original (or even from Reach) to the second and third games, since those have the most radical design departures from the original Halo.  
 
Ideally, you'll want to have played Halo 3, at the very least, before jumping headlong into Reach, just to have a sense for the pace of the game, and because some Covenant enemy types aren't really foregrounded until the last few missions of the second game and the greater entirety of the third (Maybe read up on Covenant Brutes and Covenant Drones, just so you know what they are). But there isn't anything plot-related that's really going to throw you off in Reach, as most of that game's callbacks are to the original.  
 
I wouldn't worry about it. Play Reach, then snag copies of Halo 2 and Halo 3 and do a marathon run. Reach -- Combat Evolved -- 2 -- ODST -- 3.

Reach is definitely the best in the series but if you want to get a different perspective, I don't see how playing 2 and 3 after Reach would hurt.

Considering Reach is a prequel to CE, not really, though I would suggest playing through them at some point just to get the full scope of the lore presented in the games. But from a story and gameplay story directly relevant to Reach, nah, you should be fine

If you want to play them, go right ahead.

I just bought my first 360 so I've been out of the loop on Halo since the first one on XBOX.  I have Reach coming in the mail, should I try to play through Halo 2 and 3 before I go through Reach?  I know it is a prequel so the story may not really be messed up too much but I'm also curious about if I play Reach first will I get frustrated with controls or design going back to the other two?  I also have ODST coming but will probably wait to play that until the others anyways. 
 
Just curious...