What type of equipment you purchase really depends on what type of brewing you plan on doing and how much you are willing to spend. If you plan on brewing extract brews you can get by with a relatively small amount of equipment. If, however you have a desire to end up brewing all grain, that changes things.
I started out with a simple Brewer's best equipment kit that cost around $100. It came with a fermenting bucket, bottling bucket, 2 cases of bottles, capper, and a racking cane. It didn't take me long to get an auto-siphon as it makes moving beer much easier. I also purchased a 5 gallon kettle (not beer specific) and this setup worked for quite a while.
Before too long I purchased a 5 gallon glass carboy to use as a secondary tank.
When I changed over to all grain it took more of an investment. I made a mash tun using John Palmer's design for a copper manifold and a 10 gallon Rubbermaid cooler. I also purchased an 8 gallon brew kettle with quarter turn valve and thermometer. (I kind of wish now I would have gone to the 10 gallon.) I also had to get a wort chiller. I first got an immersion chiller and HATED it. It took hours in the hot Tennessee heat to cool wort with luke-warm hose water, so I bit the bullet and purchased a Therminator. I can now take 5 gallons of boiling wort to 70 degrees in about 4-5 minutes. Pretty awesome. Best investment yet.
So, if you plan on brewing a lot and have the idea that you may want to go all grain, you have to ask yourself whether you want to purchase for the long term, or short term. My original brew pot is now my sparge water kettle (so it's being used still), but the immersion chiller is gathering dust.
Good Luck!