In terms of bluetooth, you didn't mention what you want to connect to. If you are connecting to an Android phone, normal bluetooth connections would work. There are various Android bluetooth apps that you can get that would allow you to communicate to an Arduino. I have Bluetooth Controller and Connection Terminal on my phone.
If you are connecting to an Apple phone, you would need to investigate carefully, whether your device can connect. I don't have any Apple products, but I see references to needing bluetooth 4.0 (BLE) devices for the newest phones, and having to jailbreak the phone for older phones.
I bought this module from the ebay seller NYPLATFORM, and because it is a US based seller, I got it in a few days: http://www.ebay.com/itm/HC-05-Bluetooth-Transceiver-Host-Slave-Master-Module-Wireless-Serial-6pin-/321120060216?pt=LH_DefaultDomain_0&hash=item4ac43f4338 for under $15. I primarily got it for my Teensy 3.0, since it supports 3.3 volts as well as 5 volts that my Uno uses.
I also bought a bluetooth shield from Radio Shack for my UNO (RadioShack.com Official Site - America's Technology Store) that is now $10 (when I bought it, it was $20). My sense is RS is moving away from the seeed shields like this bluetooth shield, and have lowered the price to clear the inventory. I did a search at radio shack, and only one store near me now carries the bluetooth shield. This shield does come fully assembled, unlike some other shields, which might be important if your soldering skills are a bit rusty.
For either one, you would hook up the shield to either pins 0/1 to use the hardware serial port (if you aren't using the USB device), or use the software serial support in the UNO to use other pins (the stand-alone module can use any pins, the bluetooth shield is hard wired to use pins 6 and 7). Note, there are some restrictions in software serial support, such as only being able to use one device for receiving input (http://arduino.cc/en/Reference/SoftwareSerial). Other devices like the Mega and Teensy 3.0 have more hardware serial ports (hardware serial moves more of the serial support to off board chips, and it provides buffers so it is less likely to miss characters).
The advantage of a shield is you don't have to hook up a random piece of hardware, it just fits into the UNO. The disadvantage is it isn't as flexible in terms of pin support.
There are other radio devices that aren't bluetooth, such as Radioblocks mesh networks (Dewisport - Situs Judi Live Casino, Slot Games, IDN Live Terpercaya Di Indonesia) that would be more useful if you are having a bunch of devices that need to talk to each other (bluetooth is point to point).