thinking I should uninstall JRE on (at least most of) my machines, but leave Javascript enabled. Or is that backwards ? Or is it completely wrong ?
Yup - if Java isn't needed I'd remove it.
For browser use of JavaScript the
NoScript add-on is excellent as it gives control over which site can use JavaScript
For my Firefox setup I add two of the
NoScript icons onto my toolbar giving me quick access to them.
The first image shows the
Temporarily Allow icon

The second one shows all the "components" on that site (the site in both images is ITPRO)

Edit - just noticed the ITPRO site I was on was a blog discussing Java.
Andrew Storms, director of security operations at compliance software firm nCircle, said the security problems that have recently blighted Java should prompt Oracle into overhauling the platform.
“Oracle should just redesign Java from the ground up before everyone completely loses faith in it and other Oracle products,” said Storms.
“Obviously, there’s something broken in Java development or design cycles. Oracle needs to wake up and get serious about secure software development, it’s not like there aren’t a lot of examples on how to do it right.”