Basically, there are two ways you can go about buying a rock tumbler. You can pick up the standard educational-toy model online or at most toy stores or you can get a hobbyist/professional model. What's the difference?
The Standard Model
Most toy stores carry various takes on the same model of a rock tumbler. This is a rotating tumbler that comes with rocks, grit, and some jewelry findings. This model is fun and can last indefinitely with proper care. Be advised that your choice of rock size is limited by the small rotor power and that it may be difficult to get replacement parts (e.g., broken belt from overweighted tumbler).
The toy stores carry a type of rotating tumbler, where the rocks fall over and over and over, polishing rocks in much the same manner as the ocean has for millions of years. I recommend buying a tumbler from a company that has been around a while, with an established record of quality and service. Eventually, you will need a replacement part; you want the company to still be there when that happens. Lortone offers several sizes of tumblers, some with double barrels.
Vibrational or agitating tumblers don't actually tumble the rock, but use either ultrasound or spin around the vertical axis. They cost a bit more, but have two characteristics that make them more desirable for certain users: they polish rocks much more quickly and they retain the essential shape of the rocks rather than producing only rounded rocks. They are a bit quieter, too. Raytech is an established manufacturer of vibrational tumblers (and other lapidary equipment).
Size Does Matter
… and for most people price does too, so balance the needs of your inner rock hound against the limitations of your bank account. Tumblers are sized according to the weight of the load they can continuously bear. The most common cause of rotor failure and belt breakage is improper or over-loading of the barrel. Smaller barrels hold smaller rocks (no big surprise), so larger barrels can hold both bigger rocks and more small rocks. Double barrels can be used to polish lots of rocks or to ensure a really good polish (if you reserve one barrel for that purpose).
Helpful Preparation Tips
Okay, so you've selected your tumbler! First, keep the time it takes to tumble in your mind (about a month for a rotating tumbler/ week or two for vibrating or agitating types). Get vaseline to seal the barrel against leaks! Buy extra grit (unless you want to keep that as an excuse to go out and buy more stuff). If noise is a concern, consider getting a cooler or other sound insulator to house the tumbler.