2. Try a variety of things. My first papercut I ever did was on cardstock. That just didn't work for me. Or maybe it's because it was the first papercut I ever did.
3. The first paper I used that I felt worked the best for me and I still use it often is Origami paper. It has a nice weight to it, it doesn't tear that easy and you can buy whole stacks of it in certain colors on the internet. Plus it generally has a white backing to it and you can draw or print your design right to the paper. Just search for "large origami paper black" and there are a bunch of different places to purchase this paper online.
4. The next thing I experimented with was scrapbooking paper. You can find a lot of nice colors in the scrapbooking aisle of your local craft store. Generally the paper is a little thicker, I prefer the thinner brands. Whatever you get, just make sure it's something you can see your design if you print or draw it on the paper. If you're taping a template to it, that's a different story.
5. This is the most traditional of all the papercutting papers and I only recently started using it and I love it. Silhouette paper is made specifically for silhouettes - go figure. It has a nice soft feel to it and it cuts really easily. I purchased a bunch from Dick Blick's.
That's what I use. Is there anything different that you use?