Outlook Web Access (OWA) allows any client with a compatible browser to access Exchange Server folders.
The "premium" version of OWA in Exchange 2003 looks and acts much like the Outlook 2003 desktop client, although it does not offer support for the Journal folder. The "basic" version looks more like previous versions. You may want to try both and see which is faster for the conditions your users are likely to encounter. Microsoft Exchange Server Introduction to Exchange Server 2003 has a good chart comparing the feature sets.
For Exchange 2000, you create applications using web forms. No conversion tool is available to turn Outlook forms into Exchange 2000 OWA forms. For resources and tools, see Microsoft Exchange Server Development Technologies. With Outlook 2002 and Exchange 2000, you can connect using OWA and Outlook 2002's support for HTTP mail servers (at least those that use WebDAV). The correct URL would be http://servername.domain.com/exchange/mailboxname.
OWA for Exchange Server 5.5 is also a development platform using the rendering engine in CDO. Using the Outlook HTML Forms Converter, you can convert Outlook forms to HTML forms, but any code behind the forms will have to be converted by hand to use CDO. The latest version of the Forms Converter can be downloaded as part of Exchange Server 5.5. Service Pack 4.