I've created a Codeplex site for an app I'm building and right now I just right click the entire solution folder Visual C# Express created for me, and used that.
Now in my repo I have a lot files that I'm assuming will enable the user to compile my application on their end.
I heard I shouldn't upload the /obj folder and some other things.
What things are absolutely necesary for me to commit to my repository?
You need the solution file, the C# project file(s), and all of the code files.
Basically, leave out the .suo file (with the solution), any user specific files (which will have your username appended to them, the bin\ and the obj\ folders. Everything else should be included.
You should ignore the following, by setting the svn:ignore property on your project folder:
bin
obj
*.user
*.suo
It's common practice in organizations I've worked with to also include binary resources to which we don't have the source code and are required for the build in the source control. I'm aware that this is a somewhat controversial practice but it's worked wonders for us. Usually we keep them in a solution-rooted folder named 'Resources' or the like such that they're available for each developer to use when they check out the solution.
If you would use the Standard Edition of Visual Studio you could use the AnkhSVN Plug-In, but in Express this is not possible. :-(
So what you should exclude
folder obj
folder bin
file *.user
file *.ncb
Everything else has to be in your repository.