If your ASP.NET web page is called Default.aspx, and if you code in C#, then your code behind page would be named Default.aspx.cs.
Using code behind is the preferred way of doing things in the commercial arena, at least as I see it, since presentation and coding can be separated, keeping each independent of the other.
You can place your program code right in the ASP.NET page though if you want to and avoid using code behind. Not something per say I would suggest in the commercial arena since your code is right there so anyone who has a copy of your ASP.NET pages can see your code. Web surfers won't see it though since it is compiled before being served up by the web server. It does make things harder to maintain since both ASP.NET and C# coding are mixed together.
Depending on what you are attempting to do, you may find that something like C# Standard edition or VB.NET Standard edition will suit your needs of providing a Visual Studio interface to work within. I first began my research into .NET last year with a VB.NET Standard. This year I moved on up to Visual Studio .NET Professional. I purchased my copy from an on line seller and it cost quite a bit less than the $1,000 suggested retail price. If you shop around some you can find some pretty good deals.
Hope this helps. I would suggest just taking a bit of time, doing some research while considering what it is you are trying to accomplish. I know that an IDE such as VS.NET can be expensive, but given what it can do for you it might be the best choice to take. It will all depend on how much you plan to code, the purpose your coding will serve, and how much time you want to spend doing it.