I have looked for the various components for you and here is what I have found:
The motor should be 12V so it can be run from the same supply as your receiver, and needs a reduction gear to provide enough torque for your application. Here is a suitable one. It has a max torque of 60 Newton*cm. Your door only requires 3 Newtons to lift it so it has plenty of power.http://www.ebay.co.uk/itm/25mm-12V-120R ... 46018556ea
You need a power supply with enough output to handle the starting surge current in the motor. This is a switch mode 12V 3A supply made for laptop power. Because these are made in vast quantities the price is competitive.http://www.ebay.co.uk/itm/12V-3A-AC-Ada ... 3f1ae04684
You may have your own ideas on how to lift the door, but the chain and pulley method here would be ideal. You could Google and probably get something similar for a cheaper price. http://cpc.farnell.com/mfa/917d-3/chain ... 5-00001003
Personally, I would use an alternative method. I think I would try using a piece of nylon blind cord fixed vertically to the door and kept in tension with a spring, with it wrapping a single turn round a pulley on the motor. Some rosin applied to the cord would help.
There are two main types of receiver available. The 'momentary' one where the relay is only changed over while the transmitter button is held in, and the other, a 'latched' type where the relay stays in until the other button is pressed, the relay drops out and the other relay comes in. The advantage of the latched type is that you only need a quick jab at the button to start the motor running, whereas the 'momentary' type needs the button to be pressed all the time that the motor is running.If you use the latched type then you need limit switches to stop the motor at the end of its travel. You can either fashion these yourself from springy brass strips, or you can use these microswitches. http://www.ebay.co.uk/itm/AC-250V-5A-3- ... 20c9c586e9
With a 250VAC 5A rating they should be suitable to switch 24VDC.
Do you want to go ahead?