Thanks everyone for the advice.
I've done some more research and found a page on the ST website that says miles from any program can be used for upgrades. (Since I likely won't earn enough miles for award flights and certainly don't fly enough to get higher status I'm just focusing on upgrades here.) However:
Originally Posted by Skyteam Website
The number of Miles necessary for an upgrade varies based on the frequent flyer program [...]
Since I don't want to spend hours researching how many miles are needed in each program I think I'll just go with Flying Blue (since I fly KLM the most because of my AMS-PBM flights and AMS is my home airport).
If anyone has any more advice please say so, otherwise I'll sign up for Flying Blue tomorrow.