Forum Software?

The best designed atm is xenforo by the original vbulletin crew, it also has the most active addon development community again mostly the folks that used to make all the vbulletin addons.

for free forums, i've used phpbb and simple machines... I've learned through years of administrating a forum for a friend that the bots and spammers love to attack forums so you will need to do more than just the basic download and install to keep bots and spammers out (its a never ending battle to be honest that is difficult to stop)... friend of mine had a simple machines forum and just did the basic install and nothing else. over time the bots and spammers took it over. his forum had 2500 users and at least half were fake accounts created by bots/spammers...