How to work with supercapacitors?
I have had several students who have used super cap chargers. They provide a lot of nice features like variable current limit on the charging, the particular one that I linked to will also make it so you could use 2 caps with lower voltage on each one and it will make sure you don't over voltage one.

The only down side is the chips for these are VERY small and can be difficult to solder if you aren't very experienced.