How to make apps not start up automatically on iPhone and iPad? It seems that even when I restart my iPhone, some apps will send me notifications... so how do I make them not run by itself? (kind of like making it not in the Start Up folder on Windows 7).

The reason is that Pokemon Go is eating up a lot of RAM, and with some apps starting up and/or running in the background, it causes the Pokemon Go to run very slowly sometimes, so I would like to limit the running of other apps.  (mine is iPhone 6 Plus, and I think it has 1GB of RAM. It may be that iPhone 6S Plus has 2GB of RAM and won't have this issue).
You might try turning off Background App Refresh.

Settings > General > Background App Refresh > Switch to OFF