There are three games I would recommend a GM to run a group of first timers through. (Is your group mostly new to rping?)
http://ludusnovus.net/games/LORE.pdf
If you all want a fantasy role play, this is easy to jump into. But as the DM, you (or whoever wanted to be,) would have to be creative and willing to invest lots of time in creating a setting. There is a rules system here, but not much of a world to play in. So you would have to be willing to make your own, as most LORE groups have their own personal environment. Simple and FREE, (save for dice and other accessories.)
http://www.waynesbooks.com/starwars.html
There is a good chance you guys like sci fi and Star Wars. Plus, this game gives the feeling of space fantasy, pirate/cowboy-esque adventures, and neat but easy to play through action all in one. You’ll have to buy two books, one for 10, (the GM guide,) one for 30, (second edition Star Wars D6.) But the dice will be cheap since you only need D6.
There are rules reference sheets online that you can tape to your GM screen and character sheets online. Plus, it won’t be hard to GM if you know the universe, (There are even free campaigns on the internet if you don’t like making your own.)
http://www.white-wolf.com/worldofdarkness/?line=intro
If everyone wants a more subtle game, with an edgy atmosphere, horror, angst, (oh, the angst!) and plenty of opportunities for mystery/intrigue WOD or World of Darkness is great. It is also a modern game- and in it’s nature the GM can be totally flexible with the world. So running a believable setting shouldn’t be hard. But for everything else, running WOD is TOUGH on the GM. I wouldn’t recommend it for a first time GM, but you've game before. But it is cool for a first time gamer. But yeah, can really focus on character relationships.
GURPs would work for a zombie system, but for a concept as simple as zombie, many people, (myself included,) have written their own zombie rules. Meaning A. you could make your own with little trouble and B. there are tons of zombie specific games online. Running a zombie campaign is tons of fun and not as hard as running some other game types, but I imagine you will still have a challenge as far as leading a good story. Cool thing about zombie campaigns is you don't have to prep a story, the story totally develops itself. So players have narrative control and are thus encouraged to get into the survival aspect. System is less important when this happens.