Another consideration is whether the ground the shaft passes through is solid or unstable - for example, a shaft going through limestone will generally be cut through the solid rock without ant sort of lining, whereas a shaft through something loose like shale will be lined with either drystone pack (ginging if you want to get technical...), cut stone masonry, brickwork, or timbering. Not only that. there's the size and shape of shaft to consider, for a shaft with a headgear (a winding shaft) you'd be looking at anything from about 3' round to 12' by 6' in the case of some of the really big combined pumping and winding shafts.
As for coverings - abandoned shafts can be covered by concrete caps with manholes, old railway sleepers, or if you want something a bit easier to shift , try f old corrugated iron, car bonnets, bits of railway track, brushwood, or open and surrounded by knackered barbed wire. Modern coal mine shafts get filled, but older ones might not be, and metal mines such as lead, copper, tin, etc. would tend to still be open unless they've collpased or someone has delibarately filled them in.
If you could give more of an idea of what you have in mind, as Vanoord says we can point you in the direction of something suitable, and quite possibly give photos and a detailed description too!
Follow the horses, Johnny my laddie, follow the horses canny lad-oh!