Should series connected battery cells have similar internal resistance and to what degree?
It will be almost impossible to match internal resistance since this is defined by the state of charge, temperature etc.
The best way to match the cells is to fully charge to the same endpoint voltage and then discharge each cell with the same load current (a simple load resistor) to a fixed endpoint voltage measured with a decent multimeter. This will give you the approximate capacity of each individual cell.

Select 4 cells with the closest capacity (ie time to your discharge endpoint can be used).

The internal resistance of all four cells you select is effectively in series for discharging, so the impact on the terminal voltage of the 4S under load is impacted by all the internal resistance. 

If you match the capacities of the batteries closely, you may not need a BMS. However a BMS is always better.   

This may help your understanding of the subject.