What you are trying to do has been covered many times in the forum and on the web; so many similar examples around.
Suggest you start with an Uno board that allows you to fit a lcd shield which also has buttons on it and needs no extra wiring.
It you prefer a remote lcd then you can buy just a lcd and connect it with wires.
For the Sensor, use a DS18B20, many around, the ones pre wired in a metal case probably the better than just the component. You also need a 4.7k 1/4w resistor for its complete circuit.
For the PWM fan you need a simple transistor or logic level mosfet, again a simple seach of the forum has many examples / diagrams.
Also buy yourself a breadboard and a bundle of jumper wires for making up this and other circuits you will develop.