pinetree64,
You're gonna get alot of different opinions to your question, and most of them won't be wrong, just the way the person replying does it. That said...I have refinished quite a few stocks over the years and my method has changed nearly every time because I found something that I liked better. Most of my projects have been on rifles over 50 years old so I've never had to remove polycoat, you'll have to figure that part out yourself.
Once the finish is removed I look at the worst of the damage. Is it dents(wood pushed in) or gouges and scrapes(wood missing)? If its dents I try to steam them out as much as possible with a regular household iron and a 'wet' shop towel, don't let your wife catch you using her iron for this, ask me how I know!!!! Heat the iron to high(like for cotton), take the shop towel and fold it double, dip a corner in a bowl of water, place the dripping wet corner over the dent and place the hot iron over the dent and let it steam until the corner is dry. May take more than one time to get the dent to raise as much as its going to.
Once I'm happy the dents are removed as much as they can be, I sand the stock with 220 grit on one of the rubber blocks you get at x-mart for about $2 to get rid of all the shallow scrapes, deep gouges, you have to make the call on those. For smaller areas I use a piece of sandpaper wrapped around one of those pink erasers you used to use in school when you were a kid, makes a perfect backer so you done get 'waves'. If you use a 'filler' putty, even the stainable ones show. I tend to sand them out if I can, or leave them and call it character if I can't.
Next I add color if needed as wood varies over the years and I'm kind partial to the old arsenal red/brown walnut tone. I was using Birchwood Casey's walnut stain, but it is water based and lightens too much with the next step in the proccess. My last project a guy on another forum suggested using a product called 'French Red stock filler' available through Brownells. Used it for the first time last eve so the jury is still out, but I can say I love the color if it takes.
Then I take and mix Birchwood Casey Tru-oil 50/50 with mineral spirits and 'hand rub' on the first coat and let it dry for a full 48 hours. I take the same mix and 'sand in' the next three coats with 400 grit w/d sandpaper with about 24 hours dry time and a very light buff, just down to the surface with 0000 steel wool between each coat. The sanded in coats fill the grain and give you a glass smooth finish when you're done. Then I start hand rubbing the 50/50 mix in every 24 hours til I have about 12-15 coats. If you want a gloss finish, leave the last coat dry for about 48-72 hours before you touch the stock. If you want a satin finish, lightly buff the stock with a paper soft towel after about 48 hours. If you want a flat finish, buff lightly with 0000 steel wool after about 48 hours. The 'French Red stock filler' in the last step above may eliminate the three coats of 'sand in', we'll have to wait and see how it turns out.
Basically it's a lot of hard work and elbow grease, $200 finish on a $100 .22 rifle, but it keeps me honest. Good luck with your project, however you decide to do it....