Your looking at voice recognition,RFID shield and a MP3 shield, along with a relay board. Its not impossible, but it may be tricky to get them to work together. Are you getting or do you already have an arduino, if so which one?
The two shields look relatively easy to use, but the RFID reader seems quite difficult!
I do not have any arduino hardware yet, but i figure an UNO board is what I would need to put these together.
Is there any other solution I could use besides arduino to meet my goals?
Looking at the costs of those modules, using an iPod touch or a cheap Android would seem to simplify things a lot, especially if you want accurate voice recognition, wi-fi capability (so that you can connect to the electronics that you want to switch on), etc.
Of course, if your goal is to learn/DIY electronics, then @Riva's recommended modules along with a standard Arduino Due would help you get started. The RFID reader listed there is actually reasonably easy to work with, so I suggest you give it a shot! If you read in the comments section on that Sparkfun page, the very first comment even provides sample code.