For many Web-based apps, the application server may not make that much of a difference. You could use Oracle's Application Server or IBM's WebSphere, or any other application server. The biggest thing you will want to do is to ensure that the application server supports all of your requirements. For instance, if you will be using J2EE, then you will probably not choose Microsoft's IIS. You may also want to use an application server that supports failover to a second node in case the first node goes down. Oracle's 10g App Server has no problem in a clustered/grid environment. Other products can meet this requirement as well, or maybe this isn't a requirement for your application.
I would stay away from the Oracle Rdb software. The only applications that should use this version are legacy apps specifically designed for Rdb.
Oracle Times Ten is a new Oracle product for Oracle 10g. It is Oracle's first "in-memory" database. Times Ten will give you great performance since all the data is cached in memory. However, your database should be small, as all of the data needs to fit into the server's RAM. If your database server only has 4GB of free RAM, then your Times Ten database should fit into this 4GB of available memory. Very few databases today can fit into small memory footprints.
That leaves Oracle 10g Database, which comes in two flavors, Standard Edition and Enterprise Edition. The great majority of Web applications that use Oracle use one of these two flavors of the Oracle database. Enterprise Edition contains a few features not available in the Standard Edition release. However, Enterprise Edition costs a lot more than Standard Edition. Unless you need an Enterprise Edition (EE) feature, I'd stick with Standard Edition (SE). This link shows the features in EE that are not available in SE.