I just answered this question for a friend. Means I get to cut'n paste.
I don't know what your budget is... you can easily spend a few hundred dollars for a good kitchen setup.
A large pot. Stainless steel is best, but aluminum is cheap. At least 2 gallons. The bigger, the better. Best is 6 gallons so you can do a full-wort boil where you don't have to top off the fermenter with tap water. Boiling 5 gallons of wort on a kitchen stove is a big pain though, consider getting one of those turkey fryer burner deals. The one I used to have was a 7-gallon aluminum pot and a burner. Never did fry a turkey.
A fermenter. Go for the 6 gallon variety. I used glass carboys, but I have heard very good things about the Better Bottle. If I needed another (cheap) fermenter, I'd try one out. The homebrew shop will probably tell you need a primary & secondary fermenter, but that's a myth. I do my fermentations in a single vessel and make pretty good (damn good) beer. Politely decline.
Transfer tubing, bottling wand and a racking cane. Not too much to say here - the homebrew shop will know what you need. I recommend a stainless steel racking cane over a plastic one. It's worth the extra money.
A bottling bucket.
Bottles. Five gallons of beer fills a little fewer than fifty bottles.
Sanitizer. Go for the "no rinse" variety. I switch between iodophor and 5-Star to keep the nasties on their toes. Buy in bulk.
Testing equipment. A floating thermometer or a digital thermometer on a probe. Also a hydrometer and a cheap graduated cylinder to take specific gravity readings in. Long ago I ditched the cylinder & hydrometer in favor of a refractometer. Really worth the extra money (but maybe only if you've been using a hydrometer for a while :-)
A wort chiller. After you're done boiling the wort you need to get it down to room temperature so you can toss in the yeast. The faster you do this the better. Immersion chillers are okay - they go in the kettle and you run cold water through them. Counter-flow chillers are good - they are a tube inside a tube where hot wort goes one way and cold water goes the other. Whirlpool chillers are also good, but you need an expensive pump. When I brewed in my various apartments I got a garden hose adapter for my sink because all the chillers use that fitting for the cold water. I made my first immersion chiller out of 50' of 3/8" diameter soft copper tubing, some tubing, clamps and garden hose fittings. In the very beginning I cooled my wort by immersing the pot in cold water, but that takes forever.