Hi Harty. I have been managing Ancient Semi-Natural Woodland for a little over 30 years. Ideas, advice, and considered best practice have changed over that period depending on the purpose(s) of managing the woodland. The one thing that is discussed at every forestry meeting these days is resilience. To achieve that you are aiming to have a wide diversity of species, ages, and structure.
The success of coppicing will depend on the species and ages of the trees being cut. Many trees do no coppice well when they are not cut until they are mature. On young trees you should be cutting close to the ground to encourage shooting from below the soil; on older stools you leave more stem/trunk and the new growth comes from buds on the stool. Coppicing will quickly give you a shrub understory (without browsing within a couple of years); Pollarding (at traditional height) will not provide that and will quickly increase the density of canopy - though some pollarding will at least provide a diversity of tree height.
Some areas you may decide to keep cut to provide permanent clearer areas; this requires repeated clearing of new growth. On an old railway line this will likely result in the development of bramble and thorn scrub which is a very valuable wildlife habitat but not much appreciated by the public unfortunately.
Then, of course, there's the whole aesthetic of woodland; new growth from stumps that are 3 to 4 ft high look very unnatural and in ancient woodland is something we try to avoid.
I encourage you to develop an overall management plan that people can buy into and one that can be reviewed and changed if needed. This will enable some level of continuity of objectives and methods. You can get some ideas towards that here:
Managing-Woodland-for-Biodiversity-v4-i1.pdf