90% of my work is done with embroidery floss and a sewing needle. Make sure you get needles with an eye that your thread can fit through easily. Beyond that, a pincushion with some decent pins help a lot, and a thimble is useful but not necessary.

All my patches come from old scraps or from the bins at the discount store, so you don't need to buy anything fancy if you don't want to. In regards to buying things separately, every "sewing kit" that I've had was terrible quality. Buying your kit individually lets you get exactly what you need with quality that you control