How do you choose the best lumber for framing a house?

As a baseline, no one should take on the project of framing a house without significant experience in framing smaller projects first or at a minimum have ready access to someone in the framing trade to consult with. The codes for what is required in framing are many and they do change occasionally. Have access the International Residential Code for reference

I find the question kinda funny. I expect to see dicussions on framing up a storage shed or workspace out back. That would be a reasonable DIY project. Discussing framing a house a house? Really? Ok. That implies that you are a DIY homebuilder. Acting as your own "General contractor", framing is actually one of the low precision skilled trades, along with painting. sheet rock hanging and roofing, in my personal experiance. (Having done all 3). I would be more concerned about submitting blueprints, scheduling building inspections, paying permits, managing subcontractors, etc.etc assuming you are not just building a hunters" cabin way out on your own, remote land.

Honestly when framing a residential project, pine lumber is preferred for framing. Using hardwoods is exponentially more expensive, especially if the framing is going to be covered. Furthermore southern yellow pine should be used in any structural componets unless an LVL is used.

Know your applicable building codes or a professional that does. Review with signed and sealed drawings / details. Most important – don’t take short cuts for price –

Avoid big box hardware stores while purchasing large quantities of lumber. While these stores are good for small projects, typically their lumber is not of the same quality as a lumber yard. Also most large lumber yards include free delivery and are typically cheaper than most big box stores.

The quantity of lumber required for framing even a small house is typically delivered in "bunks" or "stacks" which are standard bundles of lumber whether 2x4, 2x6, or other sizes. These bunks are made up at the lumber yard for delivery and will contain pieces of variable quality. It is up to the framer to select the best pieces for use as the studs or structural members of the frame. Generally the lower quality pieces (i.e. twisted, warped or structurally not as sound pieces) are cut up to use for blocking, cripples, backing, and so on.