There is a whole sub-forum here on home automation, that likely has people already doing things you want to do. http://arduino.cc/forum/index.php/board,16.0.html
If you are wanting to do 3-4 sensors and 3-4 switches, and remote communication, an Uno would probably suffice (14 digital pins of which 6 can be PWM, 6 analog input pins), though if you wanted to get more sensors, I would suggest going to the Mega 2560 instead, since it has more pins (54 digital pins of which 15 can be PWM, 16 analog input pins).
Another school of thought is rather than one big board, having multiple smaller boards, each with a more limited set of tasks. It depends of what you want to do, which is better in the long run.
You might want think about what remote control system you want (infrared like a TV remote, bluetooth, ethernet, wifi) as that can influence what you buy.
I would suggest scanning either http://www.adafruit.com and/or http://www.sparkfun.com to see what kinds of sensors are available,
I would imagine most of us start out with a processor and one of the bags of kit pieces that provide things like a set of LEDs, some basic sensors, a breadboard, some wires, resistors, etc. I got one from a vendor that just put every thing into a single bag with no labels, but there are places that provide better labeling for the parts. In terms of learning, I bought the book from Make.com that Radio Shack sells, and after the first day or two, never looked at it again. Instead I use the learning section of this site. Arduino has a starter kit that seems to be in short supply, but gets good press, because they have a book that covers each of the parts in the kit. However, it is a little pricey IMHO.
You might not need it immediately, but one thing you will eventually need is a soldering iron to attach (and remove) components from your setup. Also, many of the sensors/shields you get don't come fully assembled, and it is expected you would solder the pins into the boards.
One thing that I've migrated to is using prototype shields on my Uno, particularly for smaller projects. I can do the setup on the shield, and then take it off to move the processor to something else, and all of the components are still in place. Particularly as you grow a project, it is useful to have a working version, and then the setup for the next iteration, so that you can fall back to the working version if you need to. Then when the next sensor/switch is incorporated, I switch shields, and what used to be the experimenter shield becomes the working version, and the other shield becomes the experimenter shield. Otherwise you will be continually rearranging things. Here are the protoshield that I'm currently using, and the one I just bought but I haven't gotten yet, in case you don't know what I'm talking about:
- http://arduino-direct.com/sunshop/index.php?l=product_detail&p=93
- http://www.robotshop.com/dfrobot-proto-screw-shield-assembled.html
One of the key things is to think of it as an iterative process. While you have an ultimate goal in mind, take it one step at a time, adding a sensor here, setting a switch there, rather than trying to do a big bang system. In terms of development, think Agile instead of Waterfall (though I find a pure Agile system has its own negatives as well).
Look for makerspaces in your area that have other people also interested in micro-electronics.