Depends how original you want to be. Originally, I think all the cars had a tar paper over paint, with jute padding then the carpet. On the BN2, I got the kit from Moss, which came with a thick pad, and just laid it down. It's not likely this car will see much rain; we put down lots of paint and I can add something later (1st photo). For the BJ8, a few years ago I scraped out the tar paper and installed Kilmat, a Russian(!) made knock-off of Dynamat (2nd photo), then put a layer of shredded cloth water heater insulation over it (3rd photo). Then, I had floor mats custom-made by Cocomats, which are da bomb (4th photo). The floorboards will get wet, some way, somehow, so it's arguably best to have carpets, etc. removable (there originally was 'Lift-A-Dot,' I think, fasteners). I'm comfortable that the Kilmat makes as least a good a seal as tar paper, and the cloth insulation will dry but probably not as quickly as jute. Dyna/KilMat helps with soundproofing, but not much with heat insulation. My cars are drivers, esp. the BJ8 which has somewhere around 210K miles. My BN2 is a factory 100M which my late father and I restored but it's not near concours quality, but it's fun to drive. The BJ8 still has the carpet that came with it; apparently an aftermarket kit of something done by an uphosterer. Not fancy but does the job.
One unusual thing I did for the BN2 was put a layer of a 'bubble-wrap' kind of insulation with a foil side inside the doors, followed by leather. The roadsters have 'hollow' doors and I think, originally all they had was with a layer of vinyl or leather--however they were fitted--and would make a hollow sound when closed. When I close the doors on that car they make a very satisfying, meaty 'thunk.' The Moss carpeting kit was OK, not great, with some parts of the boot lining not cut exactly right.