With the
XBee Explorer module, I guess I can use directly a ZigBee module and the computer will be able to read/send message through that.
I didn't test Bluetooth over 5m. I know there are 2 power categories in specifications.
Maybe I'm already targeting ZigBee stuff. That seems more okay about distances required.
About Nano, you are just right. I read too fast.
http://arduino.cc/en/Main/ArduinoBoardFio can be the good one.
Containing connector for Polymer Lithium Ion like batteries + it contains the XBee socket at the bottom.

Anyway, I guess I'll go with
Arduino Board Fio + ZigBee module + Accelerometer + Polymer Lithium Ion like battery on the remote side, and
Xbee explorer USB + Zigbee with an antenna on the computer side.
The Polymer Lithium Ion like battery can also be charged using the USB connection on the Arduino Fio...
That seems to match well my needs.
Thanks for your precious advices here. Continuing to be interested by your opinion, of course
