K22 is correct…pillar bedding is all you need…unless its a custom stock and you want to go all the way.
If using the factory stock in either wood or synthetic, don't think you will see an accuracy gain between pillar bedding or full action bedding. I would start off with pillar bedding, see if it makes a difference or improvement in accuracy and then determine if full bedding is even necessary. But if you have the time and want to do a full bedding job don't let us stop you.
Lots of info on bedding the Lug if you search…using tape or a shim and super gluing it to the action before bedding.
Good question I have recently test fired my 6.5×55 t3 Sporter in a berserk stock that includes a recoil lug. It tested well (factory poor ammo aside). What I mean to say is that perfect bedding is not the final word on initial testing.
I will say that reloading work can make your stock work well or excellent depending on you're situation Research, and more if you can