That BM starter kit was my intro to makeup years ago. It's a great set, and it comes with application instructions. The brushes alone make it a nice value. Add a mascara (eventually eyeliner) and some lip balm or gloss, and you'll be off to a good start.
I agree, that's exactly what I started with too. THey may have improved, but the brushes were scratchy, but there are good drug stores ones you can get for now (real techniques, echo tools). Its a good place to start, get an idea of what you like/don't like and just get comfortable with makeup up, honestly (which I often think is half the battle).
A plug for cover girl lash blast as a cheap but awesome mascara. I used Lancôme for years until I found this stuff (orange container, not purple).
Totally agree. It's my favorite after trying a million brands.
I totally admit my high end mascara obsession is pointless, there are many good drugstore ones.
I realized I didn't answer other basics, I agree that besides a face kit, a blush (maybe a duo one with bronzer if possible), mascara and eye liner would be best. If you can stretch it, eyeshadows (just all over lid shade and shade for the crease).
But really, build up slowly, too many changes at once will seem weird at first (its not, promise!).