Necessary parts

First off you will need several things to build your Raspberry weather station. All in all, you should spend around 80$ or 90$ in total, without shipping. The latter part depends on your location, but all in all should be around 100$. I know, it’s not a small sum but you get a lot in return. You will be able to build your own weather station that will run on your self hosted web server. During the process you will learn many new things about Linux, WordPress, databases and programming in general.

Older Pi versions have a different number of pins. Pi 3 for example uses 40 pins. That is why there are two versions of Pi Cobbler. One for 40 pins and other for 26 pins. Make sure you buy the correct one! In the worst case, you can use this downgrade cable. I have bought some of the necessary parts from Adafruit. Her webshop is reliable, provides quality goods but the prices are quite steep. I would recommend that you buy only the Pi Cobbler kit from her. All of the other items are available on eBay for a much lower price. The goods are more or less the same and mostly come with free shipping.  Or as they say in that movie: “American components, Russian components, all made in TAIWAN!“.    
Part name Description Price
Raspberry Pi B model Your very own Raspberry Pi, it will host your website and take care of gathering and saving weather information 40$
Adafruit Pi Cobbler breakout kit (or for older Pi versions) Easily connect GPIO pins to the breadboard 8$
Breadboard wire bundle Connect the resistor and DHT22 to the breakout kit 6$
Fullk sized breadboard Used to hold all of the parts and wiring 6$
DHT22 (or DS18B20) Reading temperatures and humidity away from interferences such as Raspberry Pi 15 $
DS18B20 (or DHT22) Wired and waterproof temperature sensor 10$
4,7 k Ohm resistor Used to control the amount of current 1$
Miniature Wifi (optional!) Wireless dongle, so you need only the power cable 12$
Total without shipping: 88$-98$