Yeah you are confusing things a bit.
Activesync is the program that is used to sync data between your device and a pc. If you have a pc with XP installed then you will probably have to install Activesync software on it if it does not have it installed already. If your pc has Vista or Windows7 then you would use Windows Mobile Device Center instead of Activesync to sync your device to your pc. It does not cost anything to sync data between your device and your pc. You have to pay Verizon for a data plan in order to connect to the internet with your device. Also, you have to pay for Phone As Modem if you want to share the data connection of your device with your pc unless you do some registry hacks.