I like the gun overall. The round cheekpiece, though neat, I think detracts from the "believability" of it being an 18th c. American gun. The little stepped pointy deal at the rear of the lock panels is unusual, BUT, that sort of thing is occasionally seen on odd old guns. The treatment of the nose of the comb looks a bit "stark" to me, but it may be the photos. Also, the wood around the box lid appears rather flattish, but this also could just be the lighting in the photos.
The finish looks unfinished to me. Dull and with lots of open grain. Not too many usable ready made finishes I would recommend, other than making your own genuine, THICK boiled linseed oil!
Tried and True "Varnish oil" does work, but you have to be patient and let each THIN coat dry, dry, dry in LOTS of sunlight. You can also go to Wal Mart, in the crafts section and find a little glass bottle of Daler-Rowney purified Linseed oil. This is pretty dang good stuff, good for making paint with, and being purified, dries relatively quickly. Both of these will work better than the standard can of "boiled" linseed oil from the hardware store.
I personally don't like black grain filler, I use the oil to fill the grain. Sanding dust can also be used... let the wood fill the wood grain!
The linseed oil you have on it now (I assume it is store-bought "boiled" linseed oil) should be set in the sun to dry. For several days.... maybe weeks, depending upon how heavily it has been applied. When it is DRY, and no more oil boils out in the hot sun, and it smells different (I can tell by the smell of it when it is dry), then leave it out in the sun for another day or two, for good measure, and apply another THIN coat. Wipe the excess oil off the surface of the wood. Repeat until the grain is near filled. For the last coat or two, put it on more heavily, and let it stand on the surface. Put it in the sun to nearly dry, then cut it off the surface of the wood with burlap (this is the "hand rubbing" in a "hand rubbed oil finish"!!! LOTS of elbow grease is required). If necessary, do it again until the grain is completely filled and the surface is smooth.
Rottenstone is a polishing compound, and I don't know that it would be all that useful to you with an oil finish (though it is used as a grain filler as well by some).