To learn what you can do we should start with hardware capabilities of
the platform. The Arduino (and other uC system that uses the ATmega328 or ATmega644) have a basic set of resources that are brought out to pins on the uC --
digital inputs - You use this to read a binary signal. A voltage greater than
around two volts is a one and less than 0.8V is zero. These are used to read
the state of a binary device like a switch (mechanical, tilt, etc).
digital outputs Binary outputs. Use to turn on or off a device. LEDs, motors, etc.
With high current devices you usually need to add additional circuitry (like a transistor
or motor driver).
analog inputs These are used to read signals from analog outputs -- such as from
a sensor. Low cost temperature sensors can have analog outputs, light sensors, etc.
The analog input converts the analog signal into a digital value that can be used
by your program.
communications ports To communicate to the outside world a UART is provided. This
enables you to send ASCII strings to an external device (most people convert the UART
to a USB port). There are two other protocols available -- SPI and I2C. These are
primarily used for communications within a system. Using these two communciations
interfaces additional capabilities can be added to a system such as high current
latches, analog outputs, real-time clock, SD storage. The list of SPI and I2C
peripherals is long.
I presented an "Intro to Microcontrollers" at the MIT Barcamp in 2009.
The handout is at --
http://www.luciani.org/not-quite-ready/not-quite-ready-index.html
Now that we have a summary of most of the capabilities what are your
interests? Here are some example projects --
robots A lot of people do simple robots with their Arduino.
art A number of artists create interactive pieces with the Arduino. Add motion,
motion sensing, leds, sound
music You can create a numerically controlled oscillator (see http://wiblocks.luciani.org/docs/app-notes/nb1a-nco.html ). You could create
a midi device or an analog output sequencer that controls an analog
synth.
datalogger A number of people are doing datalogging applications. Temperature, humidity, light. Performance measurements for physical activity, etc. Energy monitoring.
control A number of people are doing CNC control with the Arduino or Sanguino.
If I were starting I would purchase a copy of "Making Things Talks" (MTT) from O'Reilly
and extend the examples. MTT works as a cookbook and a reference.
If you can send AT commands to your bluetooth module, you can also discover nearby devices.
See for example this guide. In the example they are sending commands from computer, but you can do exactly the same with your Arduino. Sending command
AT+JDDS=0
should return list of matching devices. Additionally, you can also search for specific services:
AT+JSDS=0026C3AB5A39,1101
Where 0026C3AB5A39 is MAC address of device and 1101 is code for serial port.
Best Answer
You should rather make make a cheap Arduino by yourself. By doing this, you can have it customized and use high quality parts. You can (and should) buy the original Atmega chip so you will have 100% compatibility with the software.
You will maybe [accidentally] burn the first chip to ashes (like me), but you'll get a lot of experience doing this.
Most cheap electronics have failed me. So would cheap Arduino clone, I believe. Electronic components are kind of delicate things, capacitors and transistors especially.
I know my answer is not real answer to the question, but you know, cheap hardware is random thing: you'll get a guys, that had luck (over 50% much likely) and those who didn't. My friend is of the second group and I'm pretty sure, he would sign under my answer.
Here, you can see a cheap way to make your own Arduino (cheaper than a pizza with Coca-Cola
:)): http://arduino.cc/en/Main/ArduinoBoardSerialSingleSided3