What is the best way to solder these wires to circuit board?
If you do want to solder them directly, you can make it more robust (and marginally better looking) by drilling holes wide enough for the wire + insulation to fit snugly, looping the wires through those holes and then soldering them.  This provides strain relief so that the solder joint isn't taking a significant mechanical load.

This is illustrated below, but you can also have the holes closer together, the other way round, etc - whatever's convenient.
 Image credit: Windell Oskay, CC-BY