Just been through this myself but came from a Flex/Flash background.
If you are only building ESRI JS API based apps, then as Derek suggests.
However, if you are building more general applications with a bit of mapping, can I suggest you doing the following:
1. Learn HTML5 first (HTML + CSS + JS). Not the whole thing, but enough for basic applications.
2. Introduce Dojo. Again, not the whole thing, but enough to get basic applications working so insulate yourself from browser differences and so also understand the new (ish) AMD way of doing things. I would say a firm understanding of Dojo is probably the most important part overall.
3. Then introduce ESRI JS API which I think of being plain old Dojo but with ESRI maps too.
Cheers
Ian