(Repost with altered requirements)

I am writing a HTML page that will disply data from a database I need
to know which type of database to use.
The requirements are:

1. The database will need to contain queries, be queried from within
the html page and contain relationships.
(I don't think XML will handle table relationships.)

2. The database will need to be stored client-side and therefore
accessible offline (Is ASP.NET/PHP server-side only?)

3. I don't want a message from IE6 saying that the page is insecure
like in my test version which uses VBScript to access
an Access database on my computer. 

Is not a HTML page accessing a database file on my computer always a
security risk? I have seen other pages that achieve it. Such as
Google's desktop search, which has a page that opens in IE and
searches a client-side index file/database, without IE
producing any warnings. The page address looks like this
"http://127.0.0.1:4664/&s=" which I believe means that it is using a
virtual web server on port 4664.

You might check derby...
(http://www-128.ibm.com/developerworks/opensource/library/os-ad-trifecta3/?ca=dgr-btw01ApacheDerby)

I should say that 127.0.0.1 means the web server is actually running
on the computer that is doing the searching, so it shouldn't actually
be a security risk to search your own computer.

- You get this warning because it's opened as a file on your driver
(URLs like file:///C:/MyPage.html) and IE has very restrictive (and
ridiculous) security limitation for this. But http://127.0.0.1/ or
http://localhost/, which connects to your local HTTP server, will work
just fine, and in fact it gets the least restrictions.

- ASP.NET/PHP is for server-side. But you can just use a http server
on your own computer, and you could also configure IIS or apache to
allow only localhost requests.