Picking out a new 3d printer can be very overwhelming, but so can understanding all the different types of filaments available!
Virtually all Fused Deposition Modeling (FDM) printers use 1.75mm filament. However, there are a very select few printers that use a different thickness. The first thing to do is make sure you are shopping for the proper thickness for your machine!
Next is to determine the type of filament you want to print with. PLA is the most common due to its speed and ease to print. Other popular filaments are PET-G, ABS (not near as common now as it once was) and TPU (flexible). If you are just starting out it's highly recommended that you stick with PLA.
Choosing a color sounds easy, but it too can be a big bite to take. There are single color spools (the same solid color from beginning to end), multi color spools, and specialty filaments. Multicolor filaments are typically rainbow (colors changes throughout the spool), dual color (two different colors side by side for the entire spool), tri color (three colors side by side) and quad color (four colors side by side). The rainbows and dual, tri, and quad color filaments allow you to print parts from a single spool that look great! There is also speciality filament such as glow in the dark, wood, glitter, etc. Many of these specialty filaments are abrasive and may require a hardened tip - whenever buying non standard filament do a bit of research to make sure it won't damage your machine!
Many filaments will list a tolerance on the box. Most modern filaments are +/- 0.02mm meaning the filament should range from 1.73mm to 1.77mm. However, this is not always the case as some manufacturers average the thickness through the entire spool while others will never allow the filament to fall out of tolerance at any point in the spool.
One common filament problem experienced often by people new to 3d printing is tangled spools. This almost always occurs when you let go of the end of a loose spool and it coils back on itself. This allows the end of the filament to get under a loop in the spool. Sometimes you can't see that it's now tangled and will only find out when the tangle gets tight on the spool and stops it from extruding!