NE is right, a 12 or even 10' mesh dish will work.
Of course, that all depends on what the definition of "work" is.
Premiere / CC is right in that the only way to guarantee that your signal will be rainfade and interference-free is to make it 12' (which makes the beam narrow enough that if someone lights up a fat carrier on a satellite 2 degrees away from you, you won't see it), and solid (which assures that the shape of the reflector is correct enough to insure proper gain and beam shape). The reason you want antenna gain is to have enough excess receptivity to handle signal loss when it rains - this is called fade margin.
So, if you're in a jam, it's a clear day and you have to have something, most any 10' dish will work. What will bite you by using a less-than perfect dish is the dropouts you'll get from weather and interference.
Do spend the money on a top-quality phase-locked LNB, Starguide won't work without it. DawnSat, Clear Channel or other sat vendors have them.
You mentioned roof-mounting. Although mesh dishes tend to be lighter, thus requiring a smaller mount, the disadvantage is that they flop around in the wind, i.e. give you more chance of signal errors. You probably already know this, but above a relatively low wind speed, a mesh dish looks solid in terms of wind load, and thus has no survivability advantage.
Good luck.