Much has happened with the development of RQ3 since the creation of the above writeup. For starters, the official Reaction Quake 3 website can now be found at www.reactionquake3.net.
The current (as of this writeup) version is Beta 2.25, with Beta 2.3 due along shortly. Most major bugs in terms of weapon imbalance, physics, and stability have been resolved by now. The files for Beta 2.25 can be found here:
http://www.reactionquake3.com/downloads.php#beta2.25
Of course you will need Quake 3 installed to play. If you enjoyed the fast-paced gameplay of Action Quake 2, or other realism mods, this game might be right up your alley, and the community is always in need of more players, which means you should be able to find plenty of open servers. If you're interested in taking your involvement one step beyond that, and have the skills, you could even start mapping for the game.