The nice thing about 63/37 solder is that - how do I say this - it pops liquid and pops again to solid. 60/40 and other solders have a temperature range where they will soften and get pasty but won't flow. 63/37 was developed to reduce that intermediate temperature range and melt right to a liquid state. I'd say stick to 63/37 solder but try some different brands to try the different flux formulas from the various manufacturers. In my experience flux is more important than the solder, anyway. You can make a fine solder joint using even some crap, off-brand solder if you are using good flux.
Even among the major brands of solder they are all tin and lead. The only thing that differentiates them is the flux. Kester, for example, show solders with six different flux formulas on
this page.
[EDIT]
All that talk about flux and I didn't say
what I use.
[/EDIT]