The grade of hardwood you choose for your hardwood flooring project is a personal preference, and should be based on the desired look you want to achieve, as well as budget. Each grade has it's own distinguished characteristics.
Hardwood Floor Grading Basics:
Clear Practically free of defects, made up mostly of heartwood. Most uniform color with limited small character marks. This grade will cost more than other grades.
Select or 1st grade Almost clear, with more of the normal characteristics such as knots and color variations. Unlimited sound sap wood (lighter in color).
#1 Common or 2nd grade More markings than clear or select. Light and dark colors, knots and other character marks, including sticker stain, provide a variegated appearance. Often the common grades are selected because of their more natural, rustic appearance.
#2 Common or 3rd grade The most knots, imperfections, and color variations. A natural, more affordable floor, full of character. This is your choice if many character markings are desired.
To see grading differences, scroll through these white oak photos on the NOFMA website, and read more here on wood grades.
Plainsawn
Plainsawn is the most common and least expensive method of wood flooring cuts. Plainsawn contains more variation than the other two cuts because grain patterns resulting from the growth rings are more obvious. This is the most economical method because it creates the widest boards with the least amount of waste. The flooring will tend to expand and contract more across the width of the boards.
Quartersawn
Quartersawing produces less board feet per log than plainsawing and is therefore is more expensive. The log is first cut into quarters and then sawn perpendicular to the growth rings. When quartersawn flooring is introduced to changing climates and humidity, the wood expands and contracts vertically instead of horizontal, and is therefore, a little more stable.
When shopping for flooring, if the cut is not specified, then it's pretty safe to assume the most common, plainsawn.