I've had this problem occasionally. As you say, the "ready to go" WiFi modules are expensive and usually very limited in what they let you do. Most try to do too much, like give you a UART interface to a single TCP stream. That's fine if that's all you want, but I usually have multiple TCP servers or clients, or need more out of band control than what a dumb stream gives me.
What you want is a WiFi module that interfaces at the raw network packet transport layer instead of higher level protocols. This is sortof like the MAC layer for wired ethernet. Now you can run your own network stack and do whatever you want above that.
We have done exactly this with the Microchip ZeroG WiFi modules. We implemented a ZeroG packet layer driver in our PIC 18 network stack. The rest of the stack doesn't know how packet I/O is performed, so you can set up all the TCP, UDP and other connections as you want.
The source code for our network stack is included in the free PIC Development Tools release at http://www.embedinc.com/pic/dload.htm. Of course the stack exists within the context of our firmware framework, but using all that is a good idea anyway. All the stuff I've mentioned here is available for free.
First of all, the comment regarding your intended application is very important. For this answer, I'm going to assume the you want the highest data rate possible (i.e. Wii-type controller that sends near-instantaneous data). I give you two options below. In both cases, the receiver is simple: receiver board (either another XBee or the sister board of the transmitter you are using) connected to a USB-serial converter connected to your computer.
Option 1: Really easy to build, not-so-low power
An XBee 1mw Chip Antenna can be configured to transmit at whatever datarate you need, has a max. range of 100m, and, best of all, has six on-board ADCs. You can configure the XBee to automatically sample these and transmit their values. X, Y and Z from the accelerometer can go directly into AI0, AI1 and AI2 pins on the XBee and they can both be fed with 3.3V.
- Good: You only need a battery, the accelerometer and the XBee to transmit, and another Xbee to receive.
- Bad: The XBee has 45mA peak current when transmitting.
Option 2: Not so easy to build, low power
The transmitter board you mentioned can be powered by 3.3V (according to the datasheet). Alternatively, you could use this 2.4GHz transciever. In both cases, you will need a microcontroller (easy) or an ADC with serial output (harder, will need a PCB, something along the lines of the MAX1245) to convert the analog signals from the accelerometer to digital signals for the transmitter. I recommend you use a microcontroller (Arduino Pro Mini 3.3V for prototyping, then just an ATMega328 when you're done with the design).
- Good: Low power (7-10mA).
- Bad: Will cost a lot more design time and burnt fingers.
Option 3: Stereo FM transmitters modulating 3 channels of data
This is in response to "Can I do it without converting the signals?".
- Use resistors and op-amps to bring the accelerometer's readings down to 90mVrms.
- Use two of these stereo FM transmitters, hook up X to Rin, Y to Lin, and Z to Rin of the other transmitter.
- Configure the transmitters to Tx on different frequencies.
On the receiver side:
- Aquire the FM signals and demodulate back to right and left audio. You could use something like this.
- Amplify and offset the three channels (right and left channel on one, and only right on the other) to measurable voltages (op-amps would work, but I have a feeling we just added a ton of noise to the whole thing).
- Plug these signals to any microcontroller (Arduino, if you're feeling lazy) with ADCs and send them out as serial data to your computer.
NOTE: Most FM tuners will have band-pass filters that will screw this whole idea up.
Best Answer
For serial RF over a short range (< 5 meters mentioned by OP), you can find TI CC2500 based standalone low-cost, low power modules with an ADC built in, such as this one. A search on eBay and similar sites would find you other such modules based on this IC. The size is well below the specified dimension constraints.
The device essentially takes TTL and analog inputs and pushes them in serial data form through the wireless channel to configured receivers (again, the same module can be used) at speeds up to 38.4 kilobaud. Power consumption is extremely low, but so is the sophistication of the device: It is basic but gets the job done.
An alternative IC to search for, on which similar ADC + serial RF modules are based, is the nRF9E5 which has a built in 8051 microcontroller and ADC.
Another, popular option is an XBee or ZigBee module. These come in a variety of configurations, from basic serial packet radio through Bluetooth and WiFi. Here is one such option.
Search for "Xbee Direct IO" to find suitable modules. This YouTube video shows one such module in use.
All these options are smaller than the 3 square inch size constraint, and most do not require external antennas, they use a PCB trace as an antenna.
Do check the ADC specifications in each case for your specific purposes, though, as there is a wide range of options on that front.