There are a lot of good suggestions in here. I'll just tell you my experiences.
1. Definitely use simple rosin core solder. Silver solder is HARDER to work with, not easier.
2. Use THIN solder. .022" or so. Thicker solder is much harder to work with.
3. I have a bench Ungar soldering station, and I love it. But I only have it because my company was throwing it out (fools.... it works perfectly). You don't need such an expensive iron.
4. My other iron, which I use for portable work, is an OLD Radio Shack iron. This is one of the ones from at least a decade ago or more, where you could buy the handle, and then separately buy a screw-in ceramic element for whatever heat power you wanted (mine is 25 watt). You could also buy cast iron screw-in tips for these, which I SWEAR BY. More on that below.
5. As far as I'm concerned, all the other Radio Shack irons, and I've tried a few, are sheer agony to work with. The main problem is the copper or "plated" tips they come with. In a very short time, they become pitted, warped, and won't tin worth a damn. Then you have to keep polishing/sanding/cleaning/praying to keep them clean and tinned. The cast iron tips take solder beautifully and hold up forever. I know they still sell those tips in Radio Shack as accessories. If they sell one that fits your iron, BUY IT.
6. Chisel tip, DEFINITELY. Unless you are doing ultra-fine work where you must have a precise point, chisels transfer more heat faster and are much easier to work with.
7. Wet sponge - an absolute MUST. You have to tin your soldering iron tip with some solder and keep it wiped and CLEAN while you are working, otherwise, the tip becomes a dark colored, unusable mess.
Summary:
THIN rosin core solder
Cast iron, CHISEL tip
Wet sponge.
What is my background? Well, I'm not a professional electronics assembler or anything like that, so I'm certainly no "authority." But I've done a lot of soldering - assembling things like Heathkits and Dynaco kits, as well as doing a lot of soldering on my model railroad, and building custom circuits for my model railroad with PC boards I etched myself, plus a bit of tiny surface-mount soldering where you better have steady hands and an optivisor. So my list above is based on years of practical experience, hard-learned lessons, and plenty of failures as well as successes.