Yes that is the way.
In reality you have to establish realistic goals for your rifle. If you will be making a sporter for hunting in the woods, then 2-3 moa will be acceptable (for 200 or so yards).
If you have a .312 or smaller bore and reload, you can roll some ammo that will print in the 1 moa range @100Y, especially if you slow the speed down a little.
If your goal is shooting long range, then you want a tight bore. Most folks who shoot Mosins use .311 bullets, like the 174gr .311 matchkings over some varget or H4350. A .311 bullet in a .312 bore usually works fine, but in a .313 or .314 you will have shotgun pattern groups. So all of the work and mods will be for nothing.
As for changing the barrel, it would be cheaper to just buy another rifle and then sell off that one (if it does not work out)
So, slug your barrel and see what you are working with. If you have a loose bore, then you have to decide if you want to make the investment.
If you are doing all the work yourself, then there is a chance shortening the barrel will help groups, but there is a chance grouping will be worse. If anything try 24" first, then 22" guess the only thing you can do is remaining optimistic.
Here is a mosin I did myself, 36 Tula, .312 bore chopped to 22, with ATI stock, weaver side mount and old school Redfield 1-4 scope. Bolt turned down by max_Shepperd http://maxshepherdboltproducts.com/
It will print 1.5 moa @100Y with my reloads and 2moa with most bulgarian light ball surplus. Just one example of what can be done with the Mosin.
Now this one is not my Mosin, but it sure looks nice, I found it searching for express sights http://forums.nitroexpress.com/showf...?Number=150441