Convert JPG Logo to 3-layer Vector for Family Farm

Simple task to convert simple JPEG logo into a three layer vector file for my mom's small family farm. Goal is to use the resulting art to make tshirts, hats, and other marketing material. I need to isolate the components of Creekside Natural Farm: 1. One layer for the primary "Creekside" script 2. One layer for the shadow "Creekside" script 3. One layer for the "Natural Farm" text Currently there are horizontal breaks within the letters if you try to remove them with simply "select by color" in Photoshop. I tried to "expand" the selection, but then I lost the crisp, tight lines of the letters themselves. I don't have a digital pad anymore, so I'm having trouble getting rid of those dividers and smoothing out the letters with mouse alone. I'd rather pay you to do it than sit here and still get to just an "okay" result. Farm Blog: [login to view URL]