What is the best connector for this RF 434MHz transmitter module?
Personally I've always soldered them but one thing you could consider is a 0.1" (2.54mm) terminal block which should provide a nice solid mounting. After a quick look for example I found a Multicomp MC000003 at Element 14. I measured the diameter of the pins on one of those modules at 0.5mm which is around 24 AWG. The datasheet shows it as being suitable for 20-26 AWG wire. The picture has 5 pins but that part number is a 4-pin variant:



If the main aim is to be able to change the module relatively easily another method that may be worth considering is mounting the module flush with the PCB and connecting via rectangular pads like you'd find on some edge connectors. That way if you leave a bit of space towards the module you'll be able to lift each pin individually while desoldering which should make it much easier to remove and replace them. 

A bit of double-sided tape will help keep it securely in place but you should test the transmitter range mounted both vertically and horizontally, having it mounted parallel to the ground plane and other componenets may have some effect (either positive or negative) on its operation. It's also worth doing similar tests with / without any connector you choose.