You can't switch sim cards. They're different types. If you want to use an iPhone you'll have to choose which one --- or pay for two phone plans.
As far as activating your new iPhone, use iTunes to make a backup of your iPhone 4 and then turn on the new iPhone, go thru the setup steps as instructed by the iPhone and connect to iTunes when instructed. If you want to transfer all of the iPhone 4 goodies to the new iPhone you'll have to Restore from backup instead of Set up as New. Your provider will associate your phone number & turn off the phone service to your old iPhone when it turns the service on to your new iPhone. You might need to restore more than once in order to choose the most recent backup to use.
Lots of threads about this process. Also this page at Apple Support is helpful.