I have a project I would like to lead using arduino hardware but I couldn't tell what is the best hardware choice regarding this project as well as the capabilities for future house tweaks.
I have a pellet stove driven by a wireless Room Sensor in my living room. I would like to catch the temperature information from this sensor to trigger the use of my ceiling fan (turn on/off signal will have to be done using an IR emitter to fake the remote controler).
Second project would be to control my electric shutter to open it around 7am (faking the IR remote controller to)
Third one would be to monitor and trigger all of that on my phone via an html page (I already can do that with my stove using the constructor system.
Would you have some advice on what hardware I should go for?
I suggest you start by picking the easiest of your three projects and get that working. Then you can apply the learning to the other projects.
It will be too confusing to try to advise you about 3 different things at the same time.
Can you post a link to the datasheets for any of the devices you want to interface your Arduino with? Without the technical details it will be difficult.
I like the approach you are taking of using IR to mimic the existing manual IR control of devices.
An Arduino Uno should be more than capable of what you require.
As suggested by Robin2 tackle the projects one at a time.
Once you have control of the stove adding the shutter control will be easy. For the shutter control you will probably want to add a Real Time Clock shield so that you can tell the time and also the day of the week (you might want to operate the shutter differently at weekends). Here is an example;
For remote monitoring you could implement a simple webpage on the Arduino itself. To access that you would need to add either an ethernet or a wifi shield.
In fact, I'm really starting from scratch here in term of hardware, equipments, wires etc... So if we say I go for an arduino... R3(?), should I also order a bundled starter kit to have wires and a breadboard or simply pick up some boards and wire spools anywhere I could find them?
Start with an Uno starter kit. Use it to learn; this will be a longish process.
After that, you can use it to develop your applications; you might need additional components to drive a motor, to mimic the IR or receive IR signal and for connectivity with your phone. This depends on what is in the starter kit and what you need for each project.
Once you have a project working, move it over to a more permanent construction with a Nano. Problem with the breadboard and all the wires is that it's prone to bad connections. A Nano with e.g. a screw adaptor gives a far more reliable end product.
If you are starting from scratch then getting a starter kit with an Arduino UNO R3 is a very good idea. You may or may not find a starter kit that includes all the bits you need for your project but by working through the examples you get a good understanding of programming the controller.
Build your sketches up one step at a time testing as you go and always include lots of print statements.