Ubuntu 6.06 should do you fine. It's one of the most 'user friendly' distros and will quite happily run most of the apps you've mentioned (never heard of synce). I have Ubuntu happily running on an Athlon XP 2000+ with 256Mb RAM!
Ubuntu has an Adept package manager which is very easy to use.
Afaik, there are no Linux based viruses although there are vulns. Typically these are patched by Adept. AVG and Avast both have free Linux AV tools, just in case.
Ubuntu has the Linux firewall, iptables, builtin and enabled (I think by default).
Never tried syncing my PDA though.
HTH
---------- Post added at 13:33 ---------- Previous post was at 13:31 ----------
Edit -
Link to the ubuntu forum how to on synce.