As you say, a caravan. Question is will it move? the one my brother-in-law has will never move so a simple FCU in the barn supplies all it needs, and using a switched FCU for lights although nothing wrong with a 13 amp supply to lights anyway.
Main point is some where you want a RCD, be it in the FCU or in the main consumer unit you want one some where.
If the unit can be moved, then the RCD should be in the shepherds hut so it is always RCD protected even if the supply is not, as to TT or TN, not so easy, it depends on distance to other earthed items and how the other items are earthed, in general the fire regulations means I seem to remember around 5 meters to any other building, and so best option would be TT, although allowed TN-S your not allowed TN-C-S and it is hard to know that some where there is not a combined neutral and earth.
I know electric car chargers have an auto disconnection device that allows the use of TN-C-S, however the BS7671 has not as far as I know allowed these to be used with caravans, so
NOTE: In the UK the ESQCR prohibit the use of a TN-C-S system for the supply to a caravan or similar construction.
I think still applies.
However a shepherds hut is not a building, so it does not come under the LABC, so there is no Part P, unless the supply comes from a building which would come under LABC, so you can do all the inspection and testing yourself. Of course you are responsible should anyone be injured due to what you have done, but there is no provision for the LABC to issue a completion certificate or those able to do third party inspections issue a compliance certificate. The butt stops with you, even an EICR will not remove the responsible from you, so if anything does go wrong, you need to satisfy a court that you had the ability to do the work safely, which is hard if some thing goes wrong, as the fact it has gone wrong tends to show you don't have the ability.