If I'm going to develop a web application in ASP.NET using db4o what kind of database would it be: local or remote type, and why?
I think you mean "embedded" vs "client server" (those are the two basic modes that db4o can operate in.
You will most likely want "client server" so that you can spin up multiple client sessions (perhaps one per request?).
The decision as to where to put the database depends on your scenario. Ideally, you would architect your solution so that you could do it either way via configuration. The way you can service up db40 in process in the case of a single server deployment.
However, if you need more horsepower, you could serve the db40 off of another machine to distribute the work. Note that in this case you will have more network overhead / latency.