So, now you’ve got a group and a place to play you just need something to play. Quite a lot of people, surprisingly, are system monogamous (or bigamous), while that means you’re not going to have this challenge, per se, it can still be a problem all of its own in a group that includes people that like other games and you still need to keep these things in mind in deciding what spin to give your game. If your players are all over the place on their favourite systems, games and themes then you’re going to get a clash that needs to be resolved somehow.
How to Choose
There’s a few different ways you can settle the argument of what game to play, none of them are entirely satisfactory but they should let you come to an acceptable compromise, or at least to shut the whiners up one way or the other.
GM Fiat
You’re the one running the bloody game; you’re the one that gets to choose. If the Games Master isn’t happy then nobody’s happy and if they want to play a game at all, then they’re going to have to do what you say and play what you want and tough titty if they want to do otherwise. One the plus side this establishes the Games Master’s authority right from the start and sorts out what you’re going to play with no quibbling. On the minus side, people who really, genuinely, don’t want to play a game are going to pout and possibly spoil it for everyone else.
Votes
Work out what all the different games are that people might want to play, each list them on a different piece of paper and then give each of them a score based on how much you want to play them, 1-5 or 1-10 works well. The Games Master then tots up all the scores and the one with the highest score is the one that you play. This only works if everyone’s honest and it tends to mean the same games dominate session to session unless something new really takes everyone’s fancy, but it does also tend to mean that everyone can at least tolerate whatever game it is you do end up playing.
Lucky Dip
Everyone writes down one game that they want to play and drops it into a ‘hat’ (or a dice bag, or a box or whatever). Then the Games Master draws one of the notes out of the hat and that’s what you’re going to play. This puts everyone on equal footing, gives everyone an equal chance but it can result in very unpopular choices that one person likes and everyone else doesn’t, a group predominantly of gritty horror fans playing Furry Pirates or something. Not good.
Round Robin
Use one of the methods above but only to determine what order each of the games should be played in. That gives people more time to get used to the less popular choices and makes sure that everyone gets their crack of the whip. On the downside the unpopular choice may loom over all the other games like a black cloud and motivate people to keep these other games going on longer than they should, simply to hold off the inevitable terror of Bunnies and Burrows.
Gauging the Mood
The easiest way to work out what mood people are in and what sort of game they want to play is to ask them. People aren’t always honest though and don’t always answer truthfully about how they feel or what they’re really in the mood for, plus you need to somehow collectivise everyone’s mood together and figure out a game that either makes the best of the overall mood or that hits several different emotional notes as you’re going along. That’s also difficult.
This isn’t really the sort of thing you can be advised on, empathy is something you have or you don’t have and you don’t always have the option to shift the feel of a game session from comedy to tragedy or vice versa. Just be aware of the cues going on as you play, the way people react, how ‘intense’ or ‘shallow’ they’re playing as you go along, be responsive and don’t try to force something that isn’t really working.
Postmortem Studios 
One thing with going for GM Fiat is that it presumes you have ‘A’ GM rather than a collection of them within the group. When you have a collection of people who like to both run and play then you run in to some extra problems such as
‘everyone wants to GM’ a rare one, but does happen, especially if you are in a group that enjoys a lot of systems and is always keeping an eye on new stuff that is coming out.
‘the GM that wants to but nobody likes’ GMing, like wearing lycra, is a priviledge not a right, but some people don’t see it like that and in an environment where you swap GMing around it can be quite tough to avoid having them run occasionally, especially if you don’t want to hurt their feelings by pointing out how crap at it they are…
What one of my groups tends to do is run games for 12-18 months and then as we come to the end of the run anyone who wants to run next comes up with a pitch of what they want to run and everyone talking around the idea of what they fancy. It means some stuff doesn’t get run with that group because some players just don’t want to play certain games/genres. Especially not for that length of time (we meet twice a month) although we have thrown in the odd 2-3 session filler game in the past when the main game has needed a bit of hiatus for some reason.