The servo sounds like a fine actuator. You can also get
linear servos. Otherwise a solenoid might do the trick for you, or perhaps a small motor like a VEX motor geared down with a belt drive....
As for the electronics, I just plug one of these
http://www.dx.com/p/jy-mcu-arduino-b...9#.U1cW3lfIZ-k into my Arduino and it works great... the range varies depending on walls and wall thickness, but can reach up to 30m when talking to my Galaxy SIII.
Note that as the Bluetooth Dongle uses a serial port protocol that it won't work with iOS. It might work after a jailbreak, but Apple doesn't seem to think that their users would ever want to do anything remotely technical.
If you want greater range than that, then I'd suggest a Raspberry Pi (or BeagleBone) and running a webserver on the Pi. Read the MagPi magazine, or google up different ways to use your Pi to control things "webiopi" is a good starting place... I had mine set up and turning LEDs on and off while streaming video to me from anywhere with an internet connection. Hopefully that will satisfy the range requirements!
Good luck. Sounds like a cool project. One of my students just got his lock mechanism working this weekend using RFID tags as keys, with an LCD display, and a bluetooth control to open the lock from his phone when he is on the couch. It was a pretty impressive set up... I think he's going to put together an instructable on it one day.
Jason
P.S. As far as "easiest" or "best" system for controlling it... Arduinos are more than powerful enough (even powerful enough to run a simple web server). I only suggest the Pi because a Pi+wifi dongle is less expensive than an arduino+wifi shield. There are many other great microcontrollers... the PIC comes to mind... but the Arduino platform has become a broad enough standard that you are likely to get assistance and ideas more readily with the Arduino. I'd say the Pi also has the edge over the BeagleBone in that regard, too.