One thing that I'll strongly quibble with: "Use double rather than float, unless you have a specific reason otherwise".
As a graphics programmer, I've found that single precision will do just fine in the vast majority of cases. I've also found that it's often better to try to make my code work well in the single precision while keeping an eye out for precision loss. Then I can either rewrite my math to try to avoid the precision loss, or selectively use double precision just in the parts where its needed. I think that using double precision from the start is a big hammer that's often unneeded. And using single precision buys you double the number of floats moving through your cache and memory bandwidth compared to using double precision.