This is the question I'm trying to find an answer for whenever I come to this site. Everyone seems to assume that the people reading their tutorials already know what to use and how to use it.
But to give you a condensed list based on my own experience - also, experiment so you know the quirks of each and how it behaves.
Pink Insulation Foam
Cheap, not very heavy, bruises easily but is surprisingly durable - just don't mash it. Can be tricky to cut, give yourself a tiny bit extra on measurements so you can sand any messy cuts down smooth.
I find this is great for making large, blocky shapes.
AKA Eva foam (I think) often sold as interlocking foam play/work mats, and thin sheets. The thin sheets can tear easily, but the thicker stuff is tough. Use VERY sharp scissors on this.
With a little creative painting, can be made to look like metal. Good for making armor.
Can be heated with a heat gun or similar to get rounded shapes. (Trying to do that now with my current project, a tremendous pain)
Surprisingly sturdy. I have a little experience with it, but it can be quite handy at times.
I'll be experimenting with using paper mache instead of clay to create detailed surfaces.
Can be great to use, provided...well...most tuts I've read involving wood assume you'll have the tools and a nice big workshop to play with.
Wooden dowels are often the core of my weapons, and other, weaker materials can be wrapped around them if they need a little extra support.
Lightweight and decently strong, used in ways similar to wooden dowels.
All that other stuff
There are a few other things on this site that are frequently referenced and never explained. If you see something you like, you're best bet is to E-mail the person directly and pump them for information. DO NOT let them assume you know anything about the material involved, or you won't get anywhere.