Well Unity3D IS free, Unity3D Pro isn't.
As for the web publishing. I found it really simple back when it was first released for Windows - I was intrigued and downloaded the trial.
Although I was aiming to buy the Unity3D Indie at the time, I didn't in the end as I couldn't spare the cash, but
this was a WIP thread I did in the trial, it had a web player (URL no longer works and this was on my old, now dead, laptop) but it was really easy to set up and worked really well, even though I did have an initial problem. This was 3 years ago, so I can't remember what the problem was or the solution, but I remember it being something simple.
However, an upcoming update will allow you to build to flash too.
So all of the power you get with Unity and the convenience and some of the ease can be transferred straight over into Flash.
However, it seems the OP has settled for Java, which of course is a fine choice too.