I've come up with a list that I think about when I am making a fur purse. You may be able to come up with more considerations, and feel free to post them in the comments.
1) Where will the fur pieces be sewn on the purse? If there is an area that will get a lot of wear, I use a coordinating fabric in that location. This additional fabric can also add interest to your finished piece. The below photo shows the bottom piece of my bag.
2) Will you be using zipper? If the fur is going to be near the zipper, I sew an additional non-fur piece above the fur. In the photo below, I have animal print on either side of the zipper, above the fur.
3) Will the purse be held against the body, like in a cross body bag or shoulder bag? If so, I may use a non-fur piece in the back or the part that will be against the body. In the case of the bag above, I decided to use fur on the front and back. This bag hangs low on my hips and I felt this bag style wouldn't look right without fur on both sides.
4) I like interfacing on my bags and even though this bag is a slouch bag, it can stand up because of the interfacing. Always sew the interfacing on the fur piece, NEVER iron it on as many furs will be damaged from heat. After you sew it on, cut the interfacing to the seam to reduce bulk.
5) Especially with medium to long pile fabrics, make sure you cut the fur in the seam allowance as this will reduce bulk. After you are done with a seam, you can use a needle to pull out any fur that is trapped in the seam.
5) Zippers can sometimes get lost in all that fur, especially if the fur is a long pile like this is. I like to use a decorative zipper pull for easy access (see the string of beads on the right). And it's so pretty!
6) Here's the finished furry beast! I love my bag! Here's a black one I made too.