One of the things you'll find if you are lucky enough to live near a games store that stocks Euro games like Settlers of Catan is that there are a lot of different variations of the game to choose from.
For new players, I highly recommend you start out with the basic game.
The Settlers box looks like this.
The original game supports 3 or 4 players. If you want to play with a larger group, you should also purchase the 5 to 6 player expansion pack. This will allow you to play with up to 6 players.
Most of the really great variants of Settlers are expansion packs like Cities and Knights that require you have the original game, so everyone should really start with this.
Next, I recommend the Seafarers of Catan expansion set. Sefarers introduces the notion of boats and expanding to other islands, which can make gameplay significantly more complex and interesting. You can also use the Seafarer pieces to construct interesting new board configurations that will keep the game feeling fresh even if you play quite often.
The Seafarers box looks like this. 
Again, the initial Seafarers is for 3 to 4 players, so if you want to play with a larger group, be sure to
Please note, you cannot play seafarers without the original game, so get the original first before buying this.
The final expansion set that I would highly, highly, highly recommend to everyone is Cities and Knights of Catan. Cities and Nights combined with a board using the Seafarers pieces and islands makes for the most complex and satisfying variant of Settlers. I have played this form of Catan for more than 6 hours in a row without growing bored due to the great number of strategic ways to achieve victory this setup offers. Not only does Cities and Knight introduce the Knight characters which can severe your opponents longest road and give you victory points for fending off Barbarian invasions, but the City concept is introduced which allows you to develop your civilization in different areas by upgrading your cities to have certain added special abilities. It takes a few times to really understand Cities and Knights, but once you do, you won't want to play anything else.
The Cities and Knights box looks like this.
You cannot play Cities and Knights without the Original Game, so be sure you have the original game before you buy this.
Bundle Deals
If you buy all of this and upgrade to the 5 to 6 player versions it will cost you around $180. You can save some money if you buy things in bundles. For example, you can buy a bundled Cities and Knights expansion with its 5 to 6 player upgrade for about $12 less than buying each thing individually. The original game can also be purchased as a bundle with its 5 to 6 player upgrade, as can a
You can buy the whole trio of games with their player expansions as well, if you really want to be fully decked out.
Catan Products to Avoid
The Alexander and Cheops expansion leaves me cold. I find Cheops far to slow to get going with little payoff when it finally gets underway. I haven't really played the Alexander side yet, so perhaps that is more fun, but Cheops is a snooze.
Starfarers
Sadly, I have not yet played . The reviews of this game are very good, lots of people rave about it, and I plan to purchase this soon. When I have a considered opinion I'll update this post.
Whatever you decide on, you're sure to enjoy the immersive gameplay of Catan.