The old doctor that gave it to me is dead now. He claimed to have the paperwork but mislaid it somewhere. His house was an unruly museum and archive. He told me he shot it in competitions. How do I tell if it is authentic? I really believe he at least thought it was.
There are three general categories that you're looking at for "National Match" Garands.
The Type 1 National Match rifles were built by the Arsenal as a "National Match" Rifle and fired and sold at Camp Perry to competitors. They will be documented as "National Match" Garands by the CMP. They were produced and sold up to somewhere around 1959. They were basically hand fitted stock and parts and are fairly uncommon in original condition because in the hands of competitors, they were rebuilt, rebarrelled and upgraded over their lifespan.
The Type 2 National Match garands incorporated evolving tech such as glass bedding and a hooded rear aperture. They were also arsenal built and sold at Camp Perry to competitors. The CMP would have the documentation of these as well.
The Garand collectors can tell you about the proper serial number ranges, the proper parts drawing numbers and inspector's marks. That's not me.
The third general type of garand would be those built by armorers. Included in these would be military team rifles, and civilian competitive rifles built by armorers. These, while interesting and often better shooting than the Type 1 and Type 2's are difficult to document and are probably worth the sum of their parts, unless the owner can prove that it was built by one of the legends of Garand accurizing like Don McCoy. Often times, they'll come with NM stamped barrels and/or sights, but those parts are plentiful enough that I could probably put one together like that tomorrow and peddle it to the unknowing for a pretty penny.
You could throw the Navy Garands into the same category of the Type 1 and Type 2 NM guns, but I'm not sure if they're documentable by the CMP.
How much are they worth? I'm not up to date of values...but when I checked about 10 years ago, Scott Duff was selling an unmodified Type 1 for somewhere around $2500.
For the OP, there's a whole sub category of Garand collecting for H&R. There's "arrow heads" and "postage stamps" etc. A couple of sources would be the Garand Collector's Association, and the CMP Forums. I'm not sure how active Scott Duff is anymore, but he has written some very authoratative books on Garands. FYI, None of my CMP Garands came with a crate or bayonet...not to say they don't do it now.