ADC resolution selection
It depends on the significance you need and the supported range. Consider an accelerometer that outputs 0 to 5 volts (range), and you want to measure with two decimal (significance). That would mean you would have \$5\cdot100=500\$ possible values. To get that amount of possible values in a binary number, you would need \$\lceil\log_2{(500)}\rceil=9\$ bits. In case you only want one decimal, you would have \$5\cdot10=50\$ possible values, needing \$\lceil\log_2{(50)}\rceil=6\$ bits.

You should indeed consider sample rate as well. When you use a higher resolution, the ADC will not be able to handle as much conversions as it would be when using a lower resolution. How much it differs can be find in the relevant datasheet. 

Sometimes / most of the time, you can only choose between a few resolutions, for example 8 or 16 bits. You can calculate the significance you get with, for example, 8 bits, like this: \$2^8=256\$, so we have 256 possible values. On a range of 5V, that would give a significance of \$5/256=0.0195V\$. 

In the datasheet of the accelerometer, you can find how 1V translates to the data you need. For a temperature sensor for example, you will find something like '5K/V' - this would mean one Volt difference means a 5K (Kelvin) difference. That means the output will change with 0.2V when the temperature changes with 1K. When you want a resolution of 0.1K, that would mean a resolution of 0.02V. This would mean you need \$5/0.02=250\$ values, needing \$\lceil\log_2{250}\rceil=8\$ bits.