Most of us probably started out with extract. You need a minimum amount of equipment: a kettle, a fermenting bucket, airlock and bung, racking cane and tubing, hydrometer, bottles, caps, capper, bottling bucket and a sanitizing product. You can get all of that in a kit. Read some books. With extract you learn most of the basics: boil, hop additions, cooling wort, pitching yeast, fermentation, gravity readings, bottling, etc. You can make great beer too. If you like all that you will probably want to move to all-grain (extracting your own sugars from malted grain). The cheap and easy way is batch sparging with a cooler mash tun:
http://hbd.org/cascade/dennybrew/Other than that pay attention to:
1. Sanitation
2. Pitching healthy yeast
3. fermentation Temperature
Also, if you get a kit that has you transfer to a secondary fermenter after a week or so don't bother unless you are adding fruit or aging for months. Also don't bottle after x number of days. If you think its ready take gravity readings two days apart to make sure its the same, in other words fermentation is done. Its OK for a beer to sit in a primary fermenter for several weeks.
Also also, use an online calculator to figure out how much priming sugar is needed for your style of beer. Last I knew kits came with a standard 5 oz of priming sugar which is often the wrong amount. And make sure the priming solution is mixed good in the bottling bucket by stirring thoroughly without splashing or, even better, put the solution in first and rack the beer onto it.