Hello, what follows is what I believe to be a good set of resources for using SharePoint 2003 with .NET:
The first thing I did when using sharepoint with .NET was to install the templates for visual studio, these can be found here: http://msdn.microsoft.com/library/en-us/odc_SP2003_ta/html/sharepoint_webparttemplates.asp
Once you have installed the templates you can create WebParts from within Visual Studio. The following page shows how to create a simple webpart and deploy it onto a sharepoint portal server: http://msdn.microsoft.com/msdnmag/issues/04/08/WebParts/toc.asp
The biggest pain I had when using web parts was security. SharePoint is quite a secure bugger and requires that all the assemblies you use be marked as secure, this way it stops dodgy web parts from being installed onto the server. The previous tutorial shows how to deploy and publish a web part and how to change the security but when you write your own web part it will probably whinge about security when you start accessing other objects. For example I had problems accessing a SQL Server, this is because the System.Data assembly isn’t by default secure so you have to add this onto the list of secure assemblies.
To ease the installation of web parts you can use the following page as a guide to creating installation packages that can be installed on the server. This helps by also applying any security configurations required for the web part to work: http://msdn.microsoft.com/library/en-us/odc_SP2003_ta/html/sharepoint_deployingwebparts_msi.asp
The following url gives some nice webpart examples showing how to create connectable webparts, these are webparts that can be consumers or providers of data, this way different webparts can communicate with each other. It also shows how you can add custom properties onto the properties of a web part: http://msdn.microsoft.com/library/en-us/spptsdk/html/SPPTWPFProgTasks_SV01072932.asp?frame=true
The following url shows the concept behind webparts and how they communicate: http://msdn.microsoft.com/library/en-us/spptsdk/html/SPPTWPFConcepts_SV01072928.asp?frame=true
Useful debugging resources on MSDN: http://msdn.microsoft.com/library/default.asp?url=/library/en-us/odc_SP2003_ta/html/sharepoint_debugwebparts.asp