There are plenty of servers that run the mission "Insurgency", which I quite enjoy. Most of the time, I seem to get in with a good group of guys with microphones and lots of teamwork. I was playing last night, and the insurgents managed to pin us down in a compound. We called for backup, but our backup was killed by an RPG just near the compound. We all ended up dying.
As for mods, ACE seems to be a popular mod, but it makes ArmA about 2x more complicated than it already is. It may be confusing for some new people.
Armaholic is a
great site dedicated to the ArmA series, it's been around since the introduction of ArmA: Armed Assault back in 2006 and has been my primary user-made content site since.