Take your time and do it right. Too much excitement can cause you to try shortcuts in finishing the stock, hardware, or assembly which you will later regret. In the kits I have finished I try to finish the brass parts first (sideplates, trigger guard, butt plate, patchbox if you have one, nose piece, and barrel bands (if required)) so that when you start working on the wood you will be able to fit it to the finished metal bits. If the barrel finish has tool marks or is rough cut you will need to finish it before starting the woodwork also. Next decide how you want your stock to look or fit when complete. Usually there is a lot of extra wood in the Pedersoli kits, I don't know about the traditions, but I use a small hand block plane, a shurform, or a rasp to remove wood quickly. Keep you finished metal parts handy so you can check their fit on a regular basis. Once you start getting close to where you want to be then switch to a bastard file. You will need a selection including flat, half round, triangle, and round to smooth out the various contours and get your general finished shape. Once you are close and happy with the feel and contour then you may start in with sandpaper or a sanding block. I have several of the sponge like sanding blocks but I prefer making my own with scrap wood pieces (including dowels) and wrapping them with sand paper to keep removing wood at a reasonable rate. You may need a small wood chisel or an Exacto knife set to customize and finish any reliefs or pockets in the stock. Once you are satisfied with the shape and flow just start in with ever increasing mesh grades of sandpaper until the wood feels as smooth as a baby's bottom. At this point I rub it with steel wool, again decreasing the coarseness until reaching 0000. I finish my projects with at least 7 coats of Homer Formby's Tung Oil, rubbed in between coats with the fine steel wool followed by wiping with a damp cloth to remove any residue. I usually then apply a couple of coats of Birchwood Casey Stock Sheen and Conditioner. I have sprayed the brass parts with a clear coat with mixed results but the last two I have just applied whatever gun oil I have to all the metal parts and wiped dry with pretty good results.
Good luck on your project and post some pictures when you are done.