Most home centers carry two species of construction lumber - one of three non structural species commonly called SPF (Spruce/Pine/Fir), and Douglas Fir or Southern Yellow Pine depending on your location. The SPF is lighter in color, less expensive and usually comes in fewer sizes. Though SPF is cheaper, it is also softer.
Step 1: Grain Structure
*Flat Sawn - The most common and least dimensinoally stable cut. Often used for floating panels and table tops. Most likely to warp and cup, but generally considered the most visually striking. If you know how to compensate for wood movement this is a suitable cut for any project. A board is classified as flat sawn when the annual rings are parallel, or close to parallel to the face of the board.
* Rift Sawn - Commonly used for legs in furniture as all four faces show identical grain structure. Also used for stiles and rails of doors. A board is classified as rift sawn when the annual rings are around 45 degrees to the face of the board.
*Quarter Sawn - The most dimensionally stable cut. Often used in stiles and rails of frame and panel doors and case sides. Tends to look a bit boring. Some people like boring. Also used for drawer parts. A board is classified as quarter sawn when the annual rings are perpendicular (or anything above 60 something degrees or something like that...google it) to the face of the board.
Step 2: Avoid the Center of the Tree
Never buy a board cut from the center of the tree unless you plan to cut the center out. Even if you're not working on a furniture project be aware that these boards are unstable and always crack. Center cut boards are common at home centers.
Step 3: The Rest of the Board
Avoid boards with large structural defects like cracks and unreasonably large knots. If you like knots go for it but keep in mind - knots are difficult to work and harder on your tools. Sight down the edges and faces of boards and reject those that are bowed or twisted or crooked beyond your ability to true them up.
Step 4: Be Patient
Ignorance is bliss. I've spent hours picking thru an entire pile of lumber at various home stores and found only one or two decent pieces. Other times there are more quality boards than I have room to store. I like to have a look at my favorite home stores every month and buy one or two of the best boards. With this method of buying I never have to depend on there being a high number of quality boards in stock and it gives the boards time to dry.
Step 5: Drying
Construction lumber is often very wet when it arrives at the store, especially if you live in a dry climate. You can tell by the weight of similarly sized boards which are carrying more water - try to avoid especially wet boards. It's important to allow the boards to acclimate to your climate, preferably in the space you'll eventually be working them. Some boards warp wildly as they dry, it's nice to see this happen before you've glued up a beautiful table top. With so many variables it's impossible to say how long this takes, just wait a while. Professionals use moisture gauges to determine when lumber is ready for working. This may sound unreasonable, but it's not. The more you care about the project at hand, the more you will regret rushing timber selection and preparation.
Stickering is the traditional method of stacking boards for drying. Essentially boards are stacked in a manner that allows air to flow thru the pile using thin wooden strips called stickers.
Step 6: Construction Lumber Is Lovely
These two projects represent less than $40 of lumber. I used thousands of dollars worth of tools which took me several years to accumulate.
I learned about lumber selection and preparation from this book (Workbenches, from Design and Theory to Construction and use by Christopher Schwarz).