Having fed my lime pointing addiction over the last few weeks, my overall approach is established:
To begin with the lime mortar is generally sound, if crumbly in places and needing some attention.
After hacking back there are some deep areas needing extensive filling and other areas that remain mainly intact.
Pointing is done using a 3:1 local sand to lime putty mix. The deeper areas have been filled with pinnings (small pieces of stone) and packed with lime. The joints are left roughly pointed.
After a number of days to go off, the lime mortar is hard enough to finish with a wire brush to give clean defined joints and an overall smooth undulating finish to the wall. Sharp joints and changes to levels are avoided to prevent shadowing and opportunities for water to pool.