I use a 204 Ruger for that type of shooting, specially if you are planning on shooting it a lot. Long barrel life, less heat when shooting high volume, easy to handload and a can of powder goes a very long way. Ideally a rifle that will stabilise the Sierra 39 grain Blitzkings. A real advantage of the 204 is there is no muzzle jump at all so you don't lose the sight picture which is handy if you need to make a follow up shot because you get to see the bullet splash and can make fast corrections.
Custom or factory is personal choice. If I was going custom I'd look out for an old Tikka m55 and build up from that and probably go 1:11" twist. Some of the 1:12" factory rifles are touch and go at stabilising the 39 and 40 grain bullets and you want those

Factory I'd go either a RemingtonVSSF or CZ527. The heavy barrel CZ is really balanced and doesn't feel front heavy at all. Mine is a Remington with some customisation and the action has been trued.
If you want to shoot off hand definitely the CZ, or get something in a sporter profile or fluted.