Depends on what you want the finished repair to look like, how permanent you want it to be and how much time and expense you want to put into the repair.
IMO the most permanent with the "best" results appearance wise is to have the holes TIG welded with or without plain steel filler rod, file and refinish the flat to match the barrels factory metal finish and reblue the barrel. Done this way nobody but you and the welder will know the holes were ever there.
Not quite as good appearance wise and not as permanent is to fill them with staked filler screws longer than the hole depth, file the screws flush, finish and reblue as above. A "ghost" ring where the holes were will probably still be visible though, especially if the filler screws don't take the reblue exactly the same as the rest of the barrel.
Or you can do as most folks usually do, just obtain the right size/length filler screws and Locktite them in place.
Which sights comes down to the eye of the beholder (LOL), but for most folks peep sights are an improvement over open, and brass scopes designed for traditional muzzleloaders are even better for aging eyes. The latter does not mean modern scopes for modern firearms - like me most don't think they belong on a traditional rifle.