How exciting!! As to stabilizers, many of the companies will send you a sample pack to try. Yes, it is important to use the right stablizer for the right fabric. And it's called trial and error based on how your machine reacts. You have some good sources for help already posted so I won't go back thru them. Trial and error is the rule on the embroidery thread, too. Be sure to use bobbin thread (60wt or 90wt) in the bobbin and embroidery thread (usually 40wt) on top. I keep samples of my stitchouts (another important thing to do...test stitch) and marked them as to stabilizer used, thread used, etc. I keep them in a binder in those plastic sheet protectors.
The most important thing to remember is take your time. That way you won't get frustrated (maybe) when you have bad test stitchouts (and you will, it's a given)!!
Just relax and have fun with it.
Oh, also there are great Yahoo embroidery groups you can join where you get wonderful help wth most any problem.