Feasability of an Arduino indoor positioning system using BLE
getting 1 meter accuracy with bluetooth or wifi is very ambitious (especially for 100$). The signal strength behaves very erratic and this translates in large positioning errors. Perhaps if you keep your system in one big room (with the beacons up high and in line-of-sight) it may be possible. State of the art algorithms are between 1 and 3 meters and usually use some database with RSS fingerprints together with an IMU.

As for beacons, I have used the Nordic beacons as they are very small and relatively cheap (around 30$ for a single beacon). However, they still require quite some programming in order to do positioning.

Alternatively, there is an Arduino project called pozyx about to go live on kickstarter that uses ultra-wideband for positioning. The ultra-wideband allows for very accurate distance measurements by measuring the time-of-flight (TOF) between two devices. Ultra-wideband is able to achieve an accuracy in the order of 10 centimeters. I think the full system (4 beacons and a shield) costs around 450$.