Definitely look up other questions here about controlling line-voltage devices with a micro-controller. It is seriously dangerous if you don't do it right. Look up and read about opto-isolators.
Arduino is more than you need for this task, but if this project is for learning, and that you intend to eventually tear this one down and re-use the the Arduino in other things, it is a pretty painless way to go. An awful lot of design and preparation has been done for you up front, between the on-board facilities and the available programming tools. Arduino boards run from US$20 - 60, depending; but I'm guessing (from the voltage you want to control) that you're not doing this in the US, so you'll want to check your local sources.
I'm in the middle of a project right now that I started on an Arduino Mega2560. It has a lot of memory, built in serial I/O, lots of digital I/O, analog I/O (the 'O' is PWM, though, not true D/A), boot-loader already on the board, and USB powered. Great for getting started and learning my way around with no concerns for power supplies, tool-sets, etc. Now it's running on a bare ATmega 328p chip with a battery a few LEDs, and a 7-segment numeric display. The transition was easy once I was into it and knew I could compile and download a trivial "blinky" program to prove the breadboard was working.
Good luck!