What is the difference between 4-, 5- and 6-band resistors?
The difference between 4, 5, and 6 band resistors is (mostly) the resistance tolerance. 

A four band resistor will have two bands giving two digits of the value, third band is a multiplier (number of zeros to follow the first two digits), and the fourth band indicates the tolerance - silver is +/-10%, and gold is +/- 5%

A five band resistor will have three bands giving the first three digits of the value, and will be +/- 2% or better.

A four band 1000 ohm 10% resistor may actually have a value somewhere between 900 and 1100 Ohms.  (1000 +/- 10%)

Search for an LM317 datasheet to learn about the LM317 voltage regulator, and how to calculate the voltage adjustment resistor values.

Unless the power supply kits you have include a rectifier, you must not supply them from an AC source - the LM317 needs a DC input at least 2.5 volts higher than your desired output voltage.