Embroidery on crochet afghan
Just a few thoughts:

Embroidery is usually done on a plain canvas. If the background has too much of a pattern, the embroidery will simply fade into the background. You'll want a very plain and even crochet stitch for the afghan.
Use unicolor yarn for the afghan or the embroidery might fade into the background.
If you'd like the afghan to have more of a pattern (like granny squares), insert a patch of very plain stitches where the embroidery is going to be.
Embroidery is not stretchy at all. You'll want a crocheted background that is not stretchy as well. Look for &quot;opaque&quot; crochet patterns for some inspiration.
Don't forget to crochet some test swathes to see how a pattern turns out and if you like it. This is also the best way to assess the stretchyness of the pattern and to compare different patterns.

The yarn size depends on your personal preference and the hook size depends on the yarn size and how tight you want to crochet the pattern. As a rule of thumb, thicker yarn means you crochet faster, but very loosely spun yarn can rip and tear faster once the afghan is finished and in use (this is especially important if you have kids or pets).
Embroidery is also a very broad topic... there are so many techniques that are all called &quot;embroidery&quot;.

Use a yarn that has a contrasting color to the afghan.
The yarn should be at least as thick as the one you used for the afghan.
To make the embroidery more obvious, you could embroider with 2 strings of yarn at the same time. That makes the lines thicker without doubling the number of stitches you have to do.
The example in your question is not done 100% with yarn alone, it has patches of (what looks like) felt stitched onto the canvas.