Long story short: Buy the StayBrite kit and a 100w soldering iron. That's all you need.
http://www3.towerhobbies.com/cgi-bin...&I=LXFS75&P=ML
Slightly longer story: It gets confusing when you discover that there are actually two different kinds of solder that different people called "silver soldering." The StayBrite is technically "silver-bearing" solder...usually containing about 3% silver. It comes in coils. This type of solder "flows" (i.e. "melts") at about 450˚C. Then there is another type of silver solder that comes in rods and is very expensive because it contains much more silver. This type of solder flows at 650-700˚C. Some people call this "brazing" instead of soldering.
There are other brands of 3% silver solder that can be cheaper than the StayBrite kits. For example, I frequently order this from Tower:
http://www3.towerhobbies.com/cgi-bin...&I=LXVHC4&P=ML
Also Home Depot sells 3% solder in larger coils.
The advantage of the StayBrite kit is that it comes with the bottle of flux, which is very convenient when you're just learning how to silver solder.