What Menstrual Pads do I need?

It's difficult to say how many will make a good stash for each person because there are many variables, the weight/absorbency, how heavy your flow, how often a person likes to change them, how they are washed, etc. etc.

In general you will find that these last roughly as long as an equivalent disposable pad.
You might actually find you can wear them a little longer than disposables because they are more breathable and comfortable. I also like to extend the "freshness factor" of mine by wearing the folded soaker portion against my body - then when I use the restroom I simply refold the "soiled" flap under the cleaner flap for a quick "refresh" that extends the wearability (hope that makes sense and isn't TMI). LOL

My general rules for regular menstrual use stashes are:
If you want to be able to wash every other day you will generally want to triple the lowest number of disposables you figure you use in a day. So if you'd normally use 6-10/day of a regular/heavy flow you will want about 18 of those and then maybe 2-3 overnight pads.
My sets of 18 are meant to get a typical woman through 1.5-2 days with sufficient time to wash and dry. A very frugal woman could get by with a set of 9 by washing and drying by hand as she goes. Someone who prefers to hold the pads in a cold bath and dump them in the laundry every couple of days would probably want 2 sets of 18 or a custom mix of absorbencies that might work better, say by adding an extra 10 medium/heavy pads.

When choosing pads for post partum use it will vary based on your delivery. For vaginal delivery you might find that the first 24-48 hours you have to change very often as there may be some tendency to "overflow" the sides simply because they are not as wide as the big honking disposables they give you in the hospital. But after that, as the bleeding begins to taper off they should work wonderfully for longer stretches. I think you will find they are much gentler than disposables on your tender parts and don't have the same "yucky sweaty" feel if you know what I mean.
Another cool thing to try (literally) is mist a bit of water on them with a spray bottle and stick them in the freezer for storage. This can really help with episiotomy, natural tearing, and the general vaginal soreness experienced after birth.