Does this work? Arduino Smarthome

So I thought of picking up a little "Arduino Smarthome" project.
My thought is to buy an Arduino, a touch Display, some sensors like temperature/humid Sensor and some LED stripes.
My question is now is it possible to make an interface on the Display to control the LEDs, read the data from the sensors and maybe something to control some stuff on my Computer like muting my microphone.
I know that you can do those things without the Display, but can you do it all at the same time and with an interface on the Display?
I also thought doing this with an Raspberry pi, but with an Arduino would be cheaper I think and I have more experience with the Arduino, but none with the Raspberry pi.
Also I'd like to have some room for some extensions to that.
My second thought would to have a host/master Arduino and for every single thing a standalone/slave Arduino and send the needed data to the host and then have the controls on the host/master arduino.
Is this possible?

It's possible, it's not straightforword but it's been done mainy times before. Just google "Arduino home automation" and marvel at the phletoria of results you just got..

.. and google is out of order, isn't it?

I actually googled before I started this post, but I couldn't find anything specific on the LCD topic and if this would be possible with controlling it from the LCD.
For the rest I know that it is possible, because I already did it in school. But just like how schools are the arduinos had something wrong with it and we couldn't make a LCD spit out the information from a sensor, because either the LCDs were broken or something else on the arduino.
So I just wanted to know before hand from someone who maybe already did something in that direction that in fact it is possible, before I spent a bunch of money on this

An LCD is a device showing data sent from the controller and there are also touch sencitive LCDs. Those ones more or less does the same work as a keyboard, or a set of buttons. The LCD itself does not read sensors and "spit out sensor data". Such data are collected by the controller.
No problem to build such a system. Just integrate the different components/subsystems one by one.