[Java] Enormous project, how best to get bug reports?

You will need something like that, yes. At least for internal use. There are many systems to choose from, I've for example used Trac in a couple of projects with few complaints.

Anyways - It is not necessarily a good idea to let your testers submit bugs and feature requests directly into the system. It depends on a lot of factors, your testers in particular. In many cases a separate web form can be a good way to gather the data from users. The best way is usually project specific, try to consider how you want to work with bug reports as well as what your users actually would be capable of reporting.