[SoCalSK8r]

OK,
I do this for a living (evaluate suppliers making cable assemblies).

I wouldn't use anything in the pictures above:
-as stated, if soldering iron was used for plumbing type of solder, don't use it on electronics
-I would stay away from lead free solder - people required to use lead free solder wish they didn't have to use it. It's harder to work with, requires much higher temperatures, leads to a more brittle joint, and has other characteristics which make it not a good choice

So, go to the local radio shack and pick up a new soldering iron (cheapy is fine), some leaded solder with rosin core, and you are golden.

Do not use additional flux. it can cause a lot of other issues and quite frankly isn't required unless you have some really dirty joints you are trying to bond. Even then, without proper temperatures to activate all the components in the flux, or without a good cleaning, you will leave behind chemistry that can cause corrosion.

For soldering, make sure you heat up the components you wish to solder, then bring your solder wire over to the hot component and feed it the solder. NEVER touch the solder directly to the soldering iron as this will inherently give you a cold solder joint which will fail over time.

With leaded solder, you should have a nice, shiny, smooth solder joint when finished. If it is dull, you have a cold joint.

Lastly, don't over do it with the solder. Too much solder is just as problematic as too little. You really only want enough to cover the surface and make a nice clean fillet to the mating part. A big old blob of solder is not helpful...actually it's bad.