Monitoring Network Activity

Question: What network utility can/should I use to determine if there is some hidden undesirable activity going on, say bundled into
a server software?

I am a grandpa running a small family ftp/http server for my grandchildren across Canada (hey, what else are gramps for?)

Appearances seem to show that server access is under control. I am an amateur with just enough basic understanding to get into
trouble.

My setup:
Cable fixed IP for server only
Router DI-604, virtual server for FTP (21) and HTTP (80), nothing else, ping disabled
WindowsME, email not installed
Free ZoneAlarm, allowing ftp/http only
Fastream NETFile Server from http://www.fastream.com/products.htm

Thanks,
Curious