Printer paper varies in thickness, brightness, archival quality, surface texture and coating, and fiber composition.
I have a ream of printer paper at home all the time. Besides printing, kids use it for drawing and origami, and I use it for sketching. My household consumes a ream in one to four month, depending mostly on kid's artistic activity.
Printer paper is sold by 500 sheets, or ream. Special expensive papers, like photo paper, can sell by 100 or even 20 sheets. The cheapest 20lb (75GSM) HP Multipurpose 96 Brightness Paper costs $7.50 a ream in local drugstore, and someplace as cheap as $5 a ream. Arches Infinity Smooth or Textured 345GSM costs $13.50 for a five-sheet sampler. Arches is a best brand of watercolor paper. Arches Infinity is Arches' paper with special ink-jet coating for fine art high-resolution archival prints. It is marketed as "digital fine arts paper". Everything else falls in between. Photo papers start at $13 for hundred sheets. Note that color ink jet copies cost about $1 per copy in ink.
Printer paper features and parameters: Size: most common paper size is letter size, 8 1/2" by 11" (216x279mm), with legal size (8 1/2" by 14") coming next. All printers and Xerox machines take letter size paper. The international paper standard ISO 216 is based on metric system, logical, consistent and not used in the US. A4 paper is 210x297mm. Target, Costco and various drugstores sell letter size, not A4.
Weight: the thickness of paper is described in terms of weight. Pounds in American notation (20lb or 24lb typically) corresponds to weight of a ream of 17" by 22", so the actual ream of letter-size paper weight quarter of nominal number. GMS, or g/m2 in international notation stands for gram per square meter. 20lb corresponds to 75GSM. Heavier paper is thicker, stronger and more expensive. 20lb HP multipurpose I'm running out of now is good enough for printing shopping lists and directions, as well as for endless cars line-drawn by three-year-old. It can be used for sketching in ink, but results are frustrating -- well, call it sobering. It is not thick enough to erase or to color with pencils, and too slippery for crayons. Thickness of cardstock or photo paper is expressed in mil (0.001") as well as in weight. 10.4mil is 68lb. HP, Epson, Strathmore and countless others sell papers from 20lb to photo cardstock.
Brightness: technically, it is a percentage of specific blue light reflected by paper. Brightness is expressed in percents, so 96 Brightness paper reflects 96% of light. Standard brightness is between 82 and 95. Some papers have more than 100 brightness index due to fluorescent components added to the pulp. Brighter paper looks fresh and clean, but it is not necessarily better. The reflected light can interfere with readability and put additional strain on eyes. Whiteness of the paper is different from brightness. Paper comes in warm, blue or balanced (neutral) shades of white. Human eye perceives blue shade as brighter than warm.
Archival quality or lack of it: neutral or alkaline paper is archival, while acid paper is not. You can get a handy indicator pen if you deal with undocumented paper. Archival means the paper will retain its own color and will not discolor pigment or dye on it. Best paper is alkaline buffered and says so. Pigment or dye can be archival or not, too. Laser printer pigment, graphite pencils and India ink are archival. Some markers and ball-point pens are, some aren't. Children's colored pencils are almost never archival.
Finish: the surface of paper can be coated by clay or other material or uncoated. The coating can be gloss, matte, or dull. It adds water resistance and prevents ink from bleeding into paper. That means sharper print or image, but also longer drying time and easier smudging. Some coated papers are too reflective to read comfortably and are too slippery to write. Coated papers are not suitable for pencil or pen. Photo papers are all coated with different finishes available. Uncoated papers are cheaper and more comfortable for prolonged use.
Fiber source: paper is made out of cellulose fiber and base, or glue. Cellulose comes from wood (pieces and/or wood chips and sawdust), recycled paper, or cotton (lint, recycled clothes or new cotton). The longer the fiber, the more tear- and bend-resistant paper is. Good new wood paper is alpha-cellulose paper; good cotton paper is rugs or new cotton paper. Synthetic papers are often extremely tear resistant.
See also: India ink.