Hi John
The good thing is that you have choices.
Although you then have to do your assessment.
In terms of JBI, I see that as legacy now. I suggest only to use JBI if you have experience or have existing JBI components you need to leverage.
There is a good blog here about JBI
http://trenaman.blogspot.com/2009/08/camel-vs-jbi.html
Apache ServiceMix is an ESB which ships with Camel out of the box. Camel is the light weight routing engine inside ServiceMix.
Apache ServiceMix is the server (it has start/stop scripts etc.). This is a very good fit. ServiceMix allows you to deploy and run your Camel apps.
I suggest to start out with Camel, its often the most easy to get started with. Do some prototyping. Camel is so agile and flexible
that you can run it inside the server you pick. Whether that is ServiceMix,
Tomcat, WebSphere etc.
At Camel we have a link collection you can take a look at, some of the links may talk about this topic
http://camel.apache.org/articles.html
In terms of Mule then I am biased towards Camel and will let the Mule people speak for themselves.
However I suggest to listen to the Basement coders
podcast about Camel. Link to this is from the link above.
You got some hints what they see being picked out there in real life.