You might want to pick up kits from Northern Brewer, and avoid Brewer’s Best. NB consistently makes pretty good kits, and BB consistently does not.
Here are a few more tips:
Always use fresh extract or fresh kits. Don’t buy a kit thinking oh maybe I’ll brew this one next year. Get it fresh and use it right away. Stale ingredients can give excessive flavors of caramel and banana and an odd “twang”.
Always use 100% distilled or RO water with extract beers. The extracts contain concentrated salts as part of the manufacturing process. If you use tap water or spring water on top of that, then you are essentially doubling all the salts in the beer, which can lead to strange twangy and minerally flavors in the finished beer.
Stick with dry yeast if you can help it. It is cheap, high quality, and very reliable. If you must use liquid yeast, learn how to make a yeast starter. Pitching enough healthy yeast is a critical factor in making better beer. You can get help at http://www.mrmalty.com/calc/calc.html.
Always control the temperature of your fermenting beer below 70 F. If your whole house is higher than that, then stick your fermenter into a tub with a couple inches deep of water at the bottom, and drape a wet t-shirt over the top with a fan blowing on it, to reduce the temperature inside the fermenter by about 5 degrees. The t-shirt will wick up the water and provide evaporative cooling. The water is easily replenished if/when it runs low.
You can safely skip racking to a secondary fermenter. There are few advantages. It is usually better to leave the beer on the yeast cake so that they can finish the job themselves without interference from us silly humans.
Use a little bit less priming sugar than the recipe recommends. They always give you a little too much, which can lead to gushing carbonation. If a kit gives you corn sugar, fine, just remove a tablespoon and go for it as normal. If you design your own recipes, you can skip the corn sugar and just use regular cane or beet sugar in the amount of about 5/8 cup per 5 gallons.
Finally… learn patience, especially when it comes to fermentation times. Give the yeast enough time to do their job. Don’t rush things. Relax. Give it time. It will all come together in time, and the time is often longer than the recipe says.
Oh, and uh… read. A lot. Stay on the forums. We’ve got millions of hours of experience that we can share with you, and we usually have smart folks reply within an hour or two.