Should programs be stopped accessing the internet????????

Hi
I got fed up with lots programs accessintg the inernet so formatted and reloaded windows xp pro again, then my hp printer (wireless) works office firefox and ...sygate in case anything malicious dialled out.

Even with this fresh start ive got programs going in and out, and sygate says...

Ive no idea if i should let programs access trhe intenet (doesnt this cost me money?) and anyway when sygate tells me xxx is accessing the internet dont really know what program it is.
These 3 come up all the time
NW LINK2 PX PROTOCOL DRIVER
GENERIC HOST PROCESS FOR WIN 32 SERVICES SVGHOST.EXE IS TRYING TO BROADCAST TO ... ... ... ... USING EMOTE PORT
HPLBFX EXE IS TRYING TO CONNECT TO (ROUTER IP)

Please could someone educate me on what these are, and if I just tell sygate dont allow, and is hplbfx my wireless printer, is it accessing the wirelss to print, or the internet all by itself... Id be gratefull to understand this