I think you will find the Rainfall gauge is a simple reed relay with the tipping bucket carrying a magnet to activate the reed relay on every tip. Once you have calibrated the tipping mechanism and know how many mm rainfall one tip equals, the rest of the program will be easy.
The calibration will need to show how many ml of water causes a tip, and how high that volume of water would be if tipped into a vessel with the same diameter of the top of the rain gauge. The height is the "mm of rainfall", per tip. Note the Arduino needs to count every change of state to count the tips, not just count every "high" pulse.
I would use a 10kOhm pull-up resistor on any digital Arduino input you find convenient with the switch in the rainfall sensor between the input and ground.
The anemometer will probably be similar, that is one reed relay. However the wind direction and temperature will be different and will require further investigation. More dissection of the sensors would be required to suggest anything more.
Cheers, Rob