Although its not mandatory, there is a reason for the wires being colored red and black. It has to do with convenience more than anything else.
LED is powered by direct current (DC). To make it easy to keep the Positive and Negative separate the common method is to have the positive wires red and the negative wires black.
There is a lot of solder out there!! The first thing to know is that when soldering electrical wires together...
USE ELECTRICAL SOLDER.
Today's solder comes in leaded and unleaded style. (like our gasoline )
The leaded type produces fumes that are harmful to breath.
The unleaded style solder does not flow as easily.
For LED soldering a low melt solder with rosin core is recommended.
Just like the solder selection being varied, so are the types and styles of soldering IRONS.
What type you buy will depend on what you are soldering and how frequent you will be soldering.
Low temp soldering is recommended for soldering close to the LED diodes.
The Weller 25 Watt soldering iron is a middle of the road soldering iron and is easy on the budget.