Media for Open Source SIP "PBX"?

I am looking for some piece of Open Source software to implement a SIP "PBX" on a Unix system. Ideally, it should be able to do the following:

provide SIP registry server to local SIP phones
register itself to potentially multiple outside SIP registry servers to receive SIP calls from outside under different SIP addresses (which providers might have mapped to PSTN numbers).
Provide some screening logic for incoming SIP calls
Forward incoming outside SIP calls to local SIP phones according to a definable logic
Doing so it should act as a media gateway as well, i.e. it should be a complete application-level gateway between local SIP phones and the outside world (involves e.g. some SIP header rewriting)
It should do so as well for outgoing calls
It should be able to implement a private numbering plan/call routing logic for outgoing calls including the use of different SIP caller addresses depending on the destination.
It should be able to do codec conversions, i.e. allowing the use of a compressing codec for outside incoming and outgoing calls with a local SIP phone which only supports G.711.
It should be able to color traffic by setting the IPv4 ToS bits to a defined value for outgoing VoIP packets, thus setting a basis for CoS-aware QoS.

Is Asterisk a good starting point to look for these features? Or is there any other software you can recommend taking a look at?