Reddit mentions of Fabricgenie 100% Cotton Muslin Fabric, 120-Inch, Unbleached/Natural - Sample-Swatch 4X4

FYI: I sent you lots of amazon links as I am not sure where you live or if you have access to craft stores such as Hobby Lobby or Joann Fabrics. I know for certain that I have seen most of these items cheaper at the store than what I could find online.

1. Embroidery scissors. The good ones (I.e. generally not ones that come in sewing kits) are incredibly sharp and a must. They are used exclusively for cutting embroidery floss. They make some really pretty ones that come in all sorts of colors and patterns.
   
2. A hoop or two. I personally prefer the plastic ones as they are a bit more durable and good for multiple projects. I also don't typically display my finished work inside the hoop. If she plans on making wall hangings, I would go with the wooden ones. They are typically a bit cheaper when you buy them at a craft store (I believe I have seen them from between 1-3 USD.) They have a nicer finished look and isn't that big of a deal to buy a new one when you start on your next project. I would buy her two of the wooden ones in two different sizes (a 4 inch and 6 inch one)
   
3. a box for embroidery thread. this one on Amazon that I listed is nice since it also contains the bobbins as well. These boxes usually cost about 3 USD at the craft store and are great for holding all of your different colors of embroidery floss. they often have one larger compartment which is perfectly sized to hold needles and the embroidery scissors as well. The floss bobbins are great at keeping everything organized in the box as well.
   
4. about a yard of fabric. Muslin is generally pretty cheap. For a beginner, I might also suggest Aida cloth. It it woven in a way that there is a "grid" in the cloth which makes it easier to make straight lines. It is typically used for Cross Stitch but can be used for embroidery as well. The cloth is more expensive that the muslin, and I personally don't prefer the finished look of the fabric, but it makes it easy to make straight lines and practice stitches. Someone on here also mentioned buying Fabric quarters which is a great idea. They come in a whole bunch of designs, run around 2 USD a piece, and work pretty well for embroidery.
   
5. Needles. You don't need the golden eye ones like I have listed here. Just make sure that the package says it's for embroidery as the of the needle varies depending on the type.
   
6. Now here's the hardest part of the whole thing: Embroidery floss. Most stores offer DMC brand cotton floss by the skein for about 0.48 USD. The problem is that there are literally hundreds of different colors and picking out just a few might be a bit difficult. The sets that DMC does sell are a bit pricey and aren't often set up to give you a beginner's set of colors. You could however buy an off brand set of embroidery floss that does come in a nice variety of colors and is cheaper. However, I have found that a lot of these packs have low quality thread. It often can look dull when compared to DMC brand floss. (look how Satin-y this Flower looks with the more expensive floss!) I have also heard of some people say that the colors can run when they get washed. All that said, these packs are inexpensive and great for someone just starting with embroidery as there are so many colors to choose from. Its great when you are practicing or are not 100% sure of what you are going to make yet.
   
7. transfer pen: I bought a set of those Frixion Pens that someone else mentioned in this post and I love them. They are a bit pricey. I believe that I bought my set at Target for 6 bucks. It came with 5 different colors including pink and silver which work great on dark colored fabrics. These pens are used to plan out your design on your fabric before you embroider. These pens are special in that they disappear completely with heat (such as an iron). If you don't want to go that route, they also make Water soluble markers which serve the same purpose. They don't work quite as well in my opinion as they tend to erase themselves after a few hours/days. They have the advantage of being inexpensive and work fine for small projects.
   
   I hope that all of this helps. Good luck on the shopping. I know that whatever you end up getting her she will love.