In gunsmithing we rarely use the term 'bare minimum' as this implies not doing a complete and thoroughly correct job.
I can think of 3 ways to go about your request:
1) Rechamber the factory rifle you suggest buying. A magnum bolt face is required for SAUM. Set the barrel back one thread, then open the rails, add a box (triangular windows) and follower and maybe adjust the feed ramp. Add pillars and bed the action with the bottom metal.
2) Buy the correct action, then add a top of the line barrel, a better stock than the factory one, proper box and follower. Chamber the barrel, bed the action and stock with the bottom metal.
3) Find a slightly used SAUM rifle and re-barrel it with a great barrel. Bed it.
Bare in mind that is a simplistic view of the major details and in no way should be construed as being a definitive text for the conversion.