Ceiling fans are not inherently cooling, the air movement they create blows across the skin causing moisture to evaporate and this creates the cooling effect. This is a real effect, but it works best with a bit of humidity.
The reverse or 'winter' rotation works by pushing the warm air off the ceiling back down toward the floor, where people are. The warmed air naturally rises to the ceiling and will not move unless it is pushed back down. The reverse operation of the fan draws the 'cool' air off the floor and circulates it out to the walls, minimising draughts that would happen with normal rotation and which would feel 'cool' as I mentioned above.
The quietest fans are DC, this will be specified on the box. AC fans are noisy because of the 50Hz hum, which is the power supply causing parts of the motor to 'hum'. ALL fans will make a noise on high speed due to the 'beating' of the blades in the air. Some types of blade will be noises than others, mainly flexible blades. For truly quiet operation only use a lower speed.
Remote controllers are good, but make sure it is one that is matched to the fan.
If you want to have a built in light in the ceiling fan it is possible to have the light switched by the normal light switch and separately with the remote fan control, this requires two switch wires into the ceiling fan. It is also possible to get ceiling fans where all control is through the remote; the light switch will turn all power off the the ceiling fan, but can be set up so that it will turn on the light OR start the fan!
If you do buy a ceiling fan, NEVER install it yourself (unless you are a qualified electrician). They can be very fiddly to install and wiring colours are not the same as house wiring. If you get the connections wrong it could be very dangerous, deadly in fact - the different colours are in accordance with the rules, but they are different!