Redeemer (the worker) currently supports (tested) PostgreSQL. In fact it should be possible to use any database that is supported by Hibernate but we haven't tested this so far. To install the database simply connect with your preffered tool and insert our ddl files as found in the docs directory. You should get an empty database layout.
You should bear in mind, that the frontend and map only work with PostgreSQL now. Somebody should write a generic database layer for them.
The application server is the component which will run the whole worker application. The best tested and preferred one is JBoss. It is open source and freely available. In its standard installation you just need to extract it and use the appropriate run.sh or run.bat of the bin directory to startup. If done you should reach a standard screen under http://localhost:8080/.
Please keep in mind that JBoss is an application server and not a webserver. This means that you should couple a webserver (like Apache) before it. What you need to get this working correctly is the Apache module JKConnector. There is a really fine tutorial on configuration of JBoss, Apache and JKConnector in the JBoss Wiki.