I can't speak for Missouri Star's BOMs, but Fat Quarter Shops are great for new quilters. The directions are very easy to follow, with plenty of illustrations. In addition, I've always found that they include enough fabric to cover any mistakes you might make. I'm currently making the Bristle Creek Farmhouse and just received the fourth month. It's no longer for sale on their site, but they have a Designer Mystery Quilt that they do each year and it begins in June. The price is really reasonable and if you like the fabric (this year it's Fig Tree's Ella & Ollie) then you're sure to like the BOM. It is appropriate for beginner to experienced quilters.
You could also buy some of Missouri Star's Block Magazines or watch their tutorials for lots of great ideas on what to do with your pre-cuts.
Have fun with your new hobby!