I haven’t done a lot of soldering, but I have done a ton of research on soldering. Here is my overview (feel free for anyone who actually works with this stuff on a regular basis to correct):
Kester is the “name brand, go-to” solder. From what I know, it is undetermined if it makes a big difference to use Kester as opposed to other solders. I have also seen Radioshack, Maiyum, Chicago Electric, Wyctin, etc.
The two main ratios I have seen recommended frequently for small electronics work is 60/40 and 63/37.
60/40 is probably the most common electronics soldering ratio and has high reliability and I believe (dont quote me on this) a tighter threshold for temerature.
63/37 is the solder that alot of people say you should use in place of 60/40. Honestly, the support for either seems to be about half and half (maybe a slight bias toward 63/37). 63/37 melts at a lower temperature than 60/40, and in my limited experience seems to be easier to use as a beginner. I would not recommend lead free solder unless you are in the EU in which case you’re stuck with it. It’s harder to use for a beginner as well. Also, make sure the solder has a rosin core (flux). Do not get solder with an acid core, this is for plumbing and will damage your electronics (supposedly).
Wire Gauge -
.031in/.032in (.8mm) and .025 (.6mm) seem to be the most common for small electronics work. .031/.032 is best for general work (for small electronics) and the .025 is for really tiny components.
Temperature is dependent upon metal composition and wire gauge. Just make sure you are using a soldering iron that can reach the temperature.
Price – If you dont know if it is the solder for you, get the small tube and try it out. If you dont like it, keep it for specialty work. Keep getting small tubes until you find one that is good for you, then you can buy bigger amounts.