/cgl/ - Cosplay & EGL

I need help making a logo for a sweatshirt. Here's a general mockup of what I'm hoping to make it look like.

I really like to have an embroidered look, but the only person I know with an embroidery machine has no clue how to make it and is unreliable. I'm wondering if I should learn how to do it by hand, and if so, what suggestions people have about going about it. I've heard the phrase satin stitching thrown around, so I think that might be what I'm looking for. Since it's just squares and straight lines, I wonder if there's even simple sticks of fabric or something to buy to put together in that shape.

It'll be 7x5 inches roughly, and on the chest of a sweatshirt. Not sure if it'd be better to do it on a separate fabric and iron it on, or just embroider directly into the sweatshirt (after a few tests of course).