Some of this depends upon your preferences and budget, I guess. My wife bought me a Weller WTCPT station for Christmas nearly 10 years ago, and I'm very pleased with it! For me, it actually makes soldering fun! There are much cheaper units at places like eBay, but I'm unfamiliar with them.
Assuming that you are not in Europe, use only lead based, rosin core solder. If you are in Europe, try to get some anyway!
As you probably know, NEVER use acid core solder for electronics.
Eutectic (63% Tin/ 37% Lead) will be the easiest to use, but again, the most expensive.
Kester solder is a popular brand. Personally, however, I find the fumes from their rosin core solder to be very obnoxious! I have always liked "Multicore" brand, but I guess they are out of business.