I have finished the month 1 monster (except for the small bits-I'm waiting for my mom to come and help me with those) and just finished the month 3 monster. I don't have a fancy machine (in fact, it's one of the cheapest, most basic ones. I'll have a great one someday!) and so I don't have the blanket or applique stitch. After asking around a few places, it was down to using the blind hem stitch or a simple zigzag. I did a lot of experimenting, and chose the blind hem as it's most similar to the blanket stitch (instead of a zig or "arrow" going in, it's a straight, closed stitch) My settings are just over 1 for stitch length and a little over 3 on the size of zigzag.
The biggest tip is to go slowly, and turn it by hand around the tight spots. I'm not perfect, but I am slowly improving on each piece I applique. Here's a close up of the heart so you can see what my stitch looks like.
As I work on each monster, I keep a ziploc bag handy, and keep all the little bits, fabric, pattern, etc. inside so I don't lose anything or get it confused. Simple idea, I'm sure, but one I'm happy to have thought of, as I tend to lose things and am very disorganized.