craftgrrl | embroidery guidance - stitching large blocks of colour

i'm working on my first ever embroidery project - embroidering a picture of a casette tape on a handbag i sewed this weekend.

i've only been using the sublime stitching "how to" to guide me, & i decided on using the split stitch to do the thick line border on the tape. i ordered the stitch-it kit, but it hasn't been delivered yet.

however! before the book arrives, i'm going to be ready to do the fill colour on the cassette tape. i wonder if you crafty kids can tell me: what's the best stitch technique for embroidering large-ish blocks of colour? i'm assuming that chain stitch is where it's at?

your guidance is appreciated! merci!