The transmission system
The transmission system (gears and derailleur)
Image source: http://bicycle.shimano.com
The transmission system is an other component that is important to know as its responsible of transferring your propulsion energy into the bicycle's wheels. The most important factor to look for in a derailleur is its efficiency to rapidly and precisely shifts the chain from one gear to the next. For most people, the difference will be very difficult to notice. This area of cycling has seen a major technological growth. Only the professional cyclist will require advanced derailleur. For instance, by looking at Shimano's web site, we can see a great variety of derailleur. The DEORE model for example are more aimed at professional MTB cyclist, riding in extreme conditions that puts a lot of stress on these components. For an every day use thought, the ACERA model can be sufficient.
It is hard to give any precise advice on what to look for on these components, as they are technologically very complex. The best way to evaluate them is test-riding the bicycle while extensively changing the speeds (changing gears) as you ride. There should not be significant hesitations in gear ratio changes. If you do notice problems in that area, ask the dealer to adjust it and do an other test ride. If the problem persists, be careful, it may reveal more serious derailleur problems. A few well-known brands come to mind. Shimano is presumably one of the leaders for these components. Campagnolo systems are also known to be of high quality. The test ride is your best tool of evaluation.