Thanks so much for all of this information, I hugely appreciate it. It's really pushed me to weigh up the pros and cons of each.
The games will be reasonably basic, they are just simple games for teachers to use interactively with kids. That said then, I do like the idea of using HTML5. I'll scout around and get as much info as I can because, as you say, I don't want to start heading down that route unless there are enough resources around that I can follow. If not, then I'll go down the Flash route again I think - I take your point that Flash is well established, it's likely to have everything that I need.
The other point for me is that mobile compatibility is not important, I can't see a way of it being used now or in the future for this particular site.
Again, apologies that the question was a bit vague. I was after a broad answer.
Thanks all (bar rallport) for your guidance, I appreciate it.