The HH is centerfeed top/side bolt release. If you go after a Boyds stock that is designed for a factory contour barrel you will have to open it up a little as the HH barrel is a medium heavy contour. If you get the Tacticool or thumbhole Varmints the channel will be large enough for the barrel with no work.
I don't think you would need high or extra high rings to clear the sights on the barrel. It will depend on what scope is used for sure (length), but mediums would likely work. However the rear sight is easily removed with a flathead screw driver if need be. Hope this helps a little.
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