If your users are simply going to view the Web pages and documents, they can use just about any W3C (World Wide Web Consortium) compatible browser. To participate in discussions and administration, receive alerts, edit pages and perform lookups, your users will need to be in Internet Explorer, but I was able to navigate the portal from Galeon, Mozilla and Opera. I could even get documents to open correctly on a Linux machine running Galeon.
SharePoint's indexing and searching are excellent. The indexing function not only indexes properties, titles and other meta data, it also indexes the contents of documents it recognizes--all Microsoft Office documents, XML, TIFF image files and discussions. As a bonus, Adobe offers a PDF index plug-in for SharePoint. The OCR in the TIFF indexing is some of the best I've seen.
The bad news about upgrading from SharePoint 2001 is you'll find the latest version's document profiles--the default list of data associated with a document--less accessible and more difficult to use. This is not a big deal, as profiles and document categories overlapped in SharePoint 2001, but you will have to make certain your documents are mapped into the new system intelligently. The bigger issue is that Microsoft has provided no upgrade or compatibility tool for code you wrote for SharePoint 2001. Expect to rewrite virtually all of it in the new system.
The good news about upgrading is that SharePoint no longer uses the Exchange data store; rather it stores data in SQL Server, making the user database more accessible and easier to write custom code for. The programming API in SharePoint 2003 makes a lot more sense than it did in the 2001 version, and if you're going to bulk-upload documents, you'll need it--Microsoft only supports bulk uploading of documents directly from SharePoint 2001. If you are implementing SharePoint for the first time, or continue to use bulk uploading to get documents into the system, you will need to write code to do so.