Bob,
I've done both stain and not stained. I think it depends more on the wood as to whether you stain or not. Test the wood in the barrel channel with stain vs finish and see what you think.
I personally like to fill the grain on walnut. You can use commercial fillers like Pore-O-Pac (from Woodcraft), Chambers sells filler as well, some folks even use black spray paint... Another method is to sand with the finish you'll be using, making a slurry to fill the grain, as Mitch described. Do a search here for methods, I'm sure you'll get some good info.
I've used Danish Oil, but prefer a home brewed linseed oil. That's just my preference, you can get decent results with Danish oil, I'd just practice first with a scarp piece, preferably from the same wood as your stock.
Ed