that iron will work, just dont keep the iron on anything too long especially transistors and IC chips. the heat can damage them. sometimes it will work for a couple weeks then fail. i try to keep the iron on less than 4 seconds ish depends on how hot it is. less is best. sometimes i use a heat sink to wick away the heat from a transistor leg or ic chip. an alligator clip will suffice. on old solder, sometimes it wont liquify, try adding some new solder and it will melt. i use an adjustable iron and i like it real hot so my time "in there" is shorter. you will find your equalibrium after experience. get a solder sucker, i hate using the solder wick stuff. also, i put a big fan in the window in front of me, i dont like breathing the fumes. radio shack has a bunch of different sizes of solder. i like to use the thick stuff for large areas and the thin diameter for tiny areas and solder that wont melt. those smaller irons i used to use but they quit working after awhile.
keep an eye out for cold solder joints. after all those years of heating up and cooling off, some of those "joints" form hairline cracks that inhibit electron flow. sometimes you cant see them. get in the habit of paying attention to which way the capacitor negative is pointing, sometimes the silkscreen is wrong. i use an arrow on the shelf nearby that i can turn so i dont have to "think" as much.
i use a ground strap on my wrist so i dont static shock my ic's/PCB's. its attached to my static proof mat on my worktable.
static is your enemy. just take a couple steps in the dark, in your socks on a rug and then touch a bulb with lights off and you will see.
good luck.