Yes, the 2007 Home and Student version of Office 2007 will do it. There's no upgrade for it, just the CD with Word, Excel, Power Point and One Note, stick it in and follow the install instructions.
However, if you're going to be using Office 2007 and transferring files between versions i.e. Office 2007 at home and Office 2003 somewhere else, it's worth knowing that Office 2007 uses a new file format that isn't recognised by earlier versions of Office. For Word its .docx, for Excel its .xlsx, and Powerpoint .pptx.
You can download software for earlier versions to read the new format, or alternatively, anything you may transfer can be saved in the old format. Thought I'd point it out as you mention a student version of Office 2003, and not all institutions will be using Office 2007 yet.