Hi,
If you want stepsize, then you need an analog sensir (while a pure step counter sensor could be digital).
Because mounting is not the precise, I assume it needs to be a 3 axis sensor, so software can compensate.
With an analog sensor (it may still have a digital interface) you need a much higher sampling rate than 1Hz. Thus I assume you need to process sensor data at a microcontroller close to tge sensor ... then sending the data once per second to the cell phone should work.
You should look for low power sensor, low power microcontroller and low power (wireles) data communication with cell phone.
In my eyes this is important in the early design stage, because a later change of sensor would propaply change overall performance, too. This also is true for accuracy and ruggedness.
If you want your device to be a good tool for fitness it needs to be rather precise (not necessarily accurate).
My target would be a speed precision over a complete run of maybe 1%. (My personal opinion, targeting high quality...and from my own running experience).
Specifications:
Maybe not specifications, but at least the requirement/goal should be the starting point of every design... with values and units.
Otherwise the development will take longer and you will become disappointed inbetween and need to start anew.
Klaus