Flash would be my choice for a good list of reasons. (Not the least of which is that I work for a video game company who makes Flash games).
The number of available connections to the server is a limit. Apache wasn't designed to be a game tool. It was designed to serve up web pages. Sure, it can work for what you need but the authors built the tool to handle a different sort of visitor and the max_connections is going to tap out for you too fast.
Multiplayer engines were designed for exactly your needs. Unfortunately, they are designed to interact with client side Java (not Javascript) and Flash. I like Flash.
Of course, you could place a very small, 0 pixel Flash movie on your page. Then you can continue to write your app in DHTML / Javascript. When you need to interact with the server, you interact with the Flash movie on the page and it interacts with your remote multiuser server. This would work just fine except that tools like Greasemonkey (and I think Jetpack) allow the user to manipulate Javscript on the page and they could use that to give themselves an advantage in your game. Since Flash and Java are compiled binaries, they are more difficult to manipulate so there is some layer of protection for you.
If your game was something like chess or checkers, then there is no advantage that can be gained by hacking the Javascript on the page (your move is your move) so that would be 100% secure. But if your game was a sort of shoot-em-up, and you did it in Javascript instead of Flash, then someone could manipulate the JS to give themselves better aim or something.
Start simple. There's really a lot to learn.