There are a few things that you should keep in mind when buying a drumset. If you stay with the major manufacturers, you really can't go wrong. Even the entry-level drumsets of the majors are very decent quality, and should last for years, if not a lifetime with proper care and maintenance. Some of the major drum manufacturers include Yamaha, Pearl, Tama, Ludwig, and Gretsch. There are a few manufacturers that are relatively new to the scene and are getting good reviews in the drum magazines. One of these is Taye.
The first thing I look for in an entry to mid-level drumset is good strong hardware. I look at the tom arms (the metal fixtures to hold the mounted toms in place over the bass drum) to make sure they are sturdy and strong enough to hold and last a good number of beginning years. I look at the bass drum spurs (the metal fixtures mounted near the bottom on both sides of the bass drum) to make sure the spur is mounted securely on the shell. This is an important piece of hardware because it anchors the drum securely and keeps the drum from sliding forward while being played. If there are any two items of an entry to mid-level drum set that a manufacturer may scrimp on to boost their profit margin, it is usually the bass drum pedal and hi hat stand. But that's OK. The bass drum pedal and hi hat stand usually perform well enough to get a beginning student through a year or two, and are easily exchanged for the next step up models.
A totally separate category and purchase for the drum set are the cymbals and the same advice applies — stick with the majors. Some of the majors are Zildjian, Paiste and Saiban. Over the past few decades or so, these manufacturers have made the daunting task of buying cymbals for a student a little easier (OK, a lot easier!) by introducing all-in-one beginning cymbal packages. At the least, these consist of hi hats and ride cymbal (everything a beginner would need to learn with) at a very affordable price. I have seen these packages in the two and three hundred dollar range, which is the bottom range of what a pro would pay for one top of the line cymbal. I have more than once been surprised with the quality of sound of some of these cymbals. Again, this is another step up item, and is easily exchanged for something of better quality, as the student's ear becomes more mature and sophisticated.