You need to get back to your install CD and install the SDK for Visual Studio. I assume because you've downloaded it that it would be Visual Studio Express (2008) and from memory that particular version wasn't recognized by ArcGIS as being a valid prerequisite product for the SDK. Consider using Visual Studio Express 2010 instead.
As for your license level, that will make very little difference in writing your code. You do not need a license to write the code - only to debug it. It makes life much easier if ArcGIS and the SDK are installed but they do not need to be running. Debugging can usually be done with a basic (ArcView) level of license provided you're not using extensions.
Some tips that may assist you in your endeavours:
ArcGIS is a 32 bit application, to write code for such it must be x86!
Implement a base class if you want the tool to work in
ArcMap: BaseCommand (button)
BaseTool (tool) - using
ESRI.ArcGis.ADF.BaseClasses. This gives you the ability to put a button on the frame, then if you need to insert a form for your controls.
The ArcGIS developer help is very good and should be used; there are so many interfaces it can be confusing to find the right one. Google is your best friend in finding snippets that show how the objects relate.
It seems I've made a slight mistake. For ArcGis 10.0 Visual Studio 2008 is supported:
Microsoft Visual Studio 2008 SP1 Visual Basic Express
Microsoft Visual Studio 2008 SP1 Visual C# Express
Microsoft Visual Studio 2008 SP1 (C#, VB.NET) Standard, Professional,
Microsoft Visual Studio 2010 (C#, VB.NET) Professional, Premium,
Check here ArcGis 10.0 SDK System Requirements
For other versions:
ArcGis 10.1 SDK System Requirements - VS 2008 dropped, VS2010 only
ArcGis 10.2 SDK System Requirements - VS 2012 added
ArcGis 10.3 SDK System Requirements - VS 1010 dropped, VS2013 added