A lot depends on your material costs and anticipated present (and future) fuel costs.  A good starting place is Table 2, p10 (PDF pagination) of this document. 

Fairbanks is climate zone 8, so look at the row for zone 8.  Note, those are "whole-assembly-R", not center-cavity framed wall values.  eg- A 2x12 studwall 24" o.c. withR50  high density rock wool comes in at about R33 whole-wall, after factoring in the thermal bridging of the studs.  Add 4" of Type-II (1.5lb density) rigid EPS to the exterior of that an you're there (but a double studwall approach would be cheaper.)

IRC code min is 2x4/R13 studwall + R10 continuous sheathing  or 2x6/R20 + R5 continous sheathing (either of which is about R21 whole-wall)  but that would be woefully shy of an optimal net-present-value over a 25-50 year lifecycle in Fairbanks. 

A 2x8 24" o.c. wall with R30 high density batts and wood siding comes in at about R21-R22 whole wall. That may be cheaper to build than an R20 + R5c.i. code min, but it's still just code min. Adding 3" of rigid rock wool or EPS to the exterior of that would bring it up to about R35-ish, and in your climate it's "worth it" if you plan to live there for awhile.

To hit R50-ish on the cheap usually involves a double-studwall  or Larsen Truss construction with blown fiber insulation between the studs, though some in my area have been doing that with open cell spray polyurethane about as cheaply as with blown cellulose or fiberglass.  With 2x4 double studwalls it takes about a 14-15" thick wall to hit R50 whole-wall with cellulose. With high-density rock wool or high-density fiberglass you can get there in about 13".