Ontapforrum is correct, if you are running Clustered OnTAP 8.3 or later you can browse directly to the onboard System Manager on the NAS. This would be best, as if there are any new features that you can manage they will show up there as opposed to using the outboard System Manager. The one good thing about the outobard System Manager is that it will keep track of all of your clusters, which in our case is nice since we have almost 30 of them. In that event, I'd recommend that you connect to the support site and download SM 3.1.3 before doing anything, it will be the most compatible with newer Java versions and will also get you any security and functionality updates since 3.1.2. In most (all?) cases, if there is an onboard SM on the NAS, SM should recognize it and auto-switch to it upon connection, so long as you're using the most recent offboard SM such as 3.1.3. Older versions aren't aware that an onboard SM is even possible. This gets you the "best of both worlds".
As for updating Java and keeping it compatible with SM, I've run through a lot of versions of SM over the years, and I've never run into an issue with Java incompatibility so long as you keep to at least the minimum specified versions. Just update the current Java, usually it will uninstall the older version as part of the installation. If it doesn't, then use Uninstall Programs to uninstall it.
Java is a weird animal, so there's a remote possibility that you might have to re-install SM after updating Java. This is something I've run into with a couple of Java-based apps, but I don't recall this happening with SM. I mention it here "just in case".
I hope this helps you. Good luck with your new NetApp endeavours, and don't hesitate to open a case or post here if you have any other questions.
Scott