When It comes to the subject of cheap drum sets the old saying, "you get what you pay for" really applies. A typical price for what is available currently in the cheap drums realm is approximately $200 to $400 or so. These are what I call "no name" sets because they have no reliable reputation in the drum world. The terms Junior, Kids, Beginner, and Student are nice ways of describing low quality and mediocre sounding drums at best.
With a cheap drum set what usually happens is the hardware, cymbals and heads need to be upgraded almost immediately. The pedals have very poor action. The cymbals get terribly dented because they are actually not real cymbals. The stock heads sound bad and dent very easily. These upgrades can add up very quickly when purchased individually.
This extra $200-$300 upgrade money would be better invested up front. You could then buy a nice entry level name brand set that is superior. Also if you ever need to sell, a cheap set holds very little of the original purchase price. As a drum teacher I'm often asked for my opinion and I always recommend the better drum set to avoid the upgrade hassle. If your budget allows, a brand name entry level set from a reputable company is money well spent. These drums will also come with a better warranty.
Established manufacturers include Ludwig, DW, Yamaha, Tama, Gretsch, Pearl, Premier, Sonor, Taye, PDP and Mapex. All offer excellent quality entry level drums and reliable hardware for the street price of under $1000. Doing solid internet research before purchasing is very important. Read reviews and compare prices. They also have decent resale value should you want to upgrade to a more expensive drum kit later.
For younger students the smaller versions of these drum sets is highly recommended. A 20" Bass drum and shallower toms will be much more comfortable to set up and play, with a big full sound. Having drums that are hard to reach makes playing awkward and less enjoyable and hinders technique.
Please note that quality entry level cymbal packages are sometimes included with these sets. Zildjian, Sabian and Paiste are the "big three" companies with cymbals commonly available and offer decent sound for the money. Avoid "no name" cheap cymbals.