First project, what components do I need? (Temp controlled fan)

Hi, first post here.

I don't yet have an arduino board or parts but was thinking of buying a starter kit alternatively only the parts needed for the project below.
I understand basic programming concepts but not that much about electricity.
However, I like to learn by doing things.

The purpose of this post is primarily to get help choosing a suitable arduino board as well as suitable components for the project below. No need to advice me on the programming part yet, the plan is to learn to use and program when I get the components.

What I have:
-a 3D-printer with a custom built enclosure (to prevent drafts and increase ambient temperature).
-a 12V PWM computer fan to be mounted through the back wall. (NF-F12 industrialPPC-2000 PWM)

What I want to do:
-read the temp inside the enclosure
-increase the fan speed proportional to the temp
-change the target temp by cycling through 3 pre-set settings, (for example 25°/35°/45°) using a simple button. (Note that I do not want to set the target temp via manual input but rather have 3 profiles to quickly change between. This is to match a certain ambient temperature to a certain 3D-printing filament)
-display temp on one line of a LCD and chosen profile on a second line
-use a wall outlet as a power source

What I want help with:

  1. do you see any problems with my thoughts above?
  2. what arduino board should I choose?
  3. what parts do I need to build this? LCD, tempsensor, pushbutton, some way to run the fan at 12V, what else?

Thank You

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.

links to typical parts -

For the PWM fan you need a simple transistor or logic level mosfet, again a simple seach of the forum has many examples / diagrams.

Forget about the TIP120 transistor or mosfet.
OP linked to a 4-pin fan that has all the drive electronics already inside.
Arduino just has to read temp from a temp sensor, read RPM from the fan, and output ~25kHz PWM to the fan.
Controlling 4-pin fans has been covered many times here.
Enter keywords in the searchbox on top of this page.

Thanks for your replies and my apologies for not researching enough on my own. I did search and read 4-5 posts about this before posting but was somewhat confused.

I have been doing some more reading. The fan being a 4-pin simplified things a bit.

So if I understand this correctly, this is all I need/want:
Arduino Uno (ordered)
Breadboard (ordered)
Button (ordered)
Wires (ordered)
LCD + 220ohm resistor
12V, 1A power source (already have one)

I will need to set the PWM frequency to 25kHz
Lowering the voltage going into the Arduino may reduce some heat. Maybe put some diodes in serial there.

Unless I have overlooked something?