Chuck that solder from the garage sale in the trash, unless you want to save it for soldering copper pipe joints.
All but the cheapest, lowest quality electronics solder has rosin flux in the core. As far as I know, all Radio Shack solder is rosin core. This reduces the need to manually apply flux to your surfaces in preparation to solder, and I've never needed anything but just the flux built into the solder for most small projects.
People starting out with soldering should use a lower power iron, less than 20W. If you hold your iron on a circuit board trace too long with a higher power iron, you can damage the board by separating the trace. A more experienced solderer can use higher power units. I prefer to use 25-30W irons, but I have enough experience to work quickly, and know just when the surface is warm-enough to apply solder and have it melt/flow correctly. Also the smaller the parts being soldered, the lower the power should be. Shop for an iron with a grounded plug, this can reduce static discharge at the tip of the iron.
I have an old, junked Weller soldering station that I installed a plain power outlet on, along with 2 power switches. The first switch turns on/off power to the outlet, which I plug my iron into. The other switch is wired in series between the power switch and outlet, with a power diode soldered in parallel across the switch poles. When the switch is closed, the diode is shorted, and I have full power at the outlet for the iron. When the switch is open, the diode allows half the power to get to the outlet (half-wave rectifier), making a half-power setting for the soldering iron for small components.