I would recommend finding a CNM. I believe the main difference between the two is the medical background and education/certification requirements. I believe CPMs have less requirements & do not have to attend as many births to earn their certification whereas a CNM has more schooling and clinical hours / births.
Here is a good reference (that I just found) regarding the difference between CNM and CPM: https://www.midwife.org/ACNM/files/ccLibraryFiles/Filename/000000001385/CNM%20CM%20CPM%20ComparisonChart%20082511.pdf
Granted, I'm sure you can find bad CNMs as well as CPMs as well as good of both. As you would with any provider. Regardless of the route you go, I would just make sure you research, look up reviews, interview, etc.
If you're going through insurance, you will likely have more choices with CNM. With a CPM you may be very limited on insurance coverage and may have to pay out of pocket.
ETA: Assuming you're in the states, regulations may vary by state. Some states, if you're thinking of home birth, may require a CNM. I would look into your states regulations of CPMs as well as that might be what makes the decision for you.
You might want to review the MANA and ACNM websites. They can probably provide you with a lot of information. There's definitely a lot of information out there on both types, but it's definitely a lot to sift through.
I'm also not sure if hospitals grant CPM's permission to provide care alongside a doctor if you were to need transferring, but I know not all hospitals do this with CNM's either.
I'm guessing a CPM wouldn't be able to. At most they could transfer care to an MD that has privileges, but I don't think a CPM would be granted privileges at a hospital. It's definitely worth asking a CPM about, but my best educated guess would be no.
OP, it's definitely a lot to consider, but you just have to find what works best for you.