Image source: http://www.giant-bicycle.com
Obviously, the next most important part of a bicycle is the wheels. They make it all move. You would think they are simple and do not require much attention. Think again. The wheels make a huge difference on many aspect of riding a bicycle.
The tire width is an easy parameter to verify. The wider they are, the more comfortable the bicycle will feel. Wider tires also means you add extra drag to the bicycle. This drag may seem negligible, but it is not. These few percents of energy that get lost in tire drag adds up pretty quickly as the distance you are covering increases. Race bicycles typically have 20 to 25 mm thick tires. With such narrow tires, each 10 lbs of air pressure you add or remove changes the drag factor considerably. These tires have air pressure in the 100 to 120 lbs range.
The wheels rim and spokes themselves add drag to the bicycle in term of aerodynamics turbulence. Think of the speed at which a wheel spoke runs into air as it turns. This alone adds yet a few other percent of energy loss. That is why there is an increasing amount of high-end bicycles equipped with reduced number of spokes and aerodynamically shaped rims. The goal is to limit the air turbulence to a minimum.
By now, you understand that your buying decision will be greatly influenced by the tire that best fit your riding habits. The thinner the tires, the faster will be the bicycle. On the opposite, the wider tires will ride smoother, but will reduce the bicycle speed limits.