I have used tru oil on my 32 special with great results also used on my stocks i just refeinished on my 1895 with good results. I would imagine the BLO would be the way a true woodworker/refinisher would go. Many others favor this route, I had the tru oil available and went with what I had.
The 32 special is a 1952 version that was in horrible shape from a pawn shop. bubba carved his name in the stock and forearm and I had to refinish because I could not walk around with a rifle with someone elses name on it. the 1895 is a remlin I bought about 1-1/2 yrs ago and was sent back to remlin to fix an apparent crack in the receiver (see sticky in 45-70 section I started the alert) I could not get any accuracy with the rifle and scout set-up so when I took it all the way down I decided the faux checkering had to go and I liked the perch belly on the 32 so I mimicked that when I did it. surely the wood is nicer than with the faux checkering.
My Pop's was a true woodworker/woodsmith and if he was with us today he would have told me I should have used the BLO I am sure, but the tru-oil was easy to work with and with many coats and steel wool in between it turned out better than I would have expected.
the 336 is a satin finish 9steel wool last step) and the 1895 I left glossy due to the pretty eagle cuff from MO member.
Building muzzleloaderes I used a combination of Boiled Linseed Oil and Tru Oil. The BLO takes longer to dry and Tru Oil is a Linseed Oil with an drying excellerator. As for walnut, Tru oil makes agreat finish and brings out the color. Also Tru oil is a fairly tough finish and scratches can be easily sanded out and repaired if no stain is added.
I've had very good results with Tru Oil but I like BLO also. Personally I think Tru Oil is a little easier to deal with but I think either one would look nice if you put the time into it. I heard somewhere that Tru Oil is a mixture of Linseed Oil and Tung oil but I have no idea how much truth there is to that.
In the process myself. This is off my New Rossi 410. Took off the shoe polish with 320. Moved on to 400 and ended almost 5 hrs later with 600 grit sandpaper. Put on a coat of English Chestnut stain tonight. Now trying to decide what next. I was thinking about 4 coats of Spar Urathane but now I may consider the BLO or True Oil. If this turns out decent, Im gonna do my other Rossi as well.
If you do any sanding on birch or walnut you should give the stock a damp rag wipe between grades of sandpaper, stain application after thorough drying and before your final finish as a check. The damp wipe will swell some wood cells on the surface ("raise the grain") so your final wipe after your last sanding should no longer result in any grain raising. If you don't do this the BLO or Truoil or Tung oil will raise the grain and not allow a really nice totally smooth finish. So, don't raise the grain with your oil finish, do all that before the oil.
As Burk mentions you defeather any wood with a damp rag to get the best results. More so with the white woods as they are generally stained and the stain will not lift the grain. Stock finishing depends on what one wants to achieve and in some cases the wood itself. I do not often go much below 220 anymore but that is due to the work on Maple in ML's. You can get the wood so slick it does not take stain well, been there seen that. Also a plain Jane fairly straight grained stock has fewer issues than a fancier one.