Since I am just beginning this new adventure..and my hands are not very co-operative when cutting, I am wondering if you use and reccommend a fabric cutter for triangles, etc.? Also, does anyone use a Cricut for cutting out appliques?

I like the Accuquilt Go! for cutting out triangles. They come out perfect, and all the corners are nipped off so they are easy to pair up accurately.

May I recommend a book call Patchwork Skills & Techniques by Dorothy Wood. (ISBN 0-7548-1319-3).Lorenz Books.
This little book is a wealth of information for a new quilter.
In it she explains about sewing squares together then cutting. Doesn't always apply but where it does it saves so much time, heartache and frustration.
Welcome to the wonderful world of quilting and to this forum.

I use my AccuQuilt Studio to cut everything! I can't even imagine the quilting process without it anymore!

Accuquilt is an expensive investment if one is just starting to quilt. Need to build that stash.

My favorite triangle piecing method is Brenda Henning's Triangulations - it works for half-square and quarter-square triangles. You basically layer your fabrics with a sheet printed from her computer program and stitch on the lines, then cut the triangles part. It is a really accurate method. You might also try Triangle Trimmers from Fons and Porter - although I have not used that method, I have friends that do.