Bug Tracking And Project Management Solutions?

I’m always looking for ways to make things more efficient.

At the moment the way we handle development internally is not as efficient as it should be. It’s also quite hard to track “issues”.

So what I’m trying to find is some kind of software solution that allows us to do all that (and more) efficiently.

The kind of scenario we’re dealing with is a bit like this:

Staff requests > Developers
Client requests > Staff
Management > Developers
Management / Staff / Developers > 3rd party vendor

That may not be particularly clear …

Say there’s an application that our staff use internally and they want to either give feedback on an existing feature or request a new one.
Other applications / interfaces are customer facing and again, being able to get feedback and track it properly would be very beneficial.

At the moment someone (be they staff or a client) may make a feature request or submit feedback. It isn’t easy to track the progress of it and it’s impossible to show the user what’s going on with their request.

Ideally the software would allow us to have internal and external projects and expose the bugs / issues for certain ones, but with a reasonable level of control. For example, if there was a security bug you wouldn’t want to publicise it until you’d had a chance to deal with it etc., etc.

Another facet which is very important is triage / management. If you’ve got a finite number of developers working for you then you need to prioritise their workload.

Software that I’ve come across to date include solutions like Fog Bugz. There are two problems with Fog Bugz:

• audience – it seems to be aimed at the hardcore geek primarily. While that would work fine for our more technical staff and possibly even some of our technical users, it wouldn’t work for either our non-technical staff nor our non-technical users
• costs – while I appreciate that you need to pay for things, the problem is that we don’t have unlimited funds (who does?).

Hosted vs Outsourced?
I’d prefer to be able to host the solution “inhouse”, though I would be open to use some form of SAAS.

Technology?
If it’s “inhouse” then it needs to be using some form of LAMP. No Java or Ruby on Rails please.

So if anyone has any suggestions or recommendations please please share them

Update: Thanks for all the comments. Unfortunately a few of them got trapped by MT’s spam filters, but they’re all published below now.