I know VS2012 is able to use .NET framework 4.5. VS2010 can handle till .NET 4.0. I've seen the changelog between the frameworks, but is there any advantage according the use of Tridion 2013 when using framework 4.5?
One advantage you would have in using VS2012 (or up) is that you can use the .NET framework 4.5, now for most Template Building Blocks and Event Handlers (using the TOM.NET API), there isn't much if anything at all that would be an advantage for you.
So unless you require the new features of 4.5 (I remember we needed it for something in the Template Building Blocks for the SDL Tridion Reference Implementation, but I forgot what it was), you would be equally good off with using the .NET 4.0 framework. With regards to which version of Visual Studio you should use, there I would be tempted to go for the latest at all times (although personally I didn't bother to upgrade from VS2012 to VS2013 yet at the time of writing this, but will soon when I get my new laptop ;o).