Word 97 documents will open fine with Word 2007. You can then decide whether to save it in Word 97-2003 format, i.e., .doc, or the newer Word 2007 format, i.e., .docx. If you want, you can set Word 2007 to use the Word 97-2003 format by default.
Installing two versions of Office on the same computer can be done but it's not recommended. If you want to install both, do a careful read of this:
http://support.microsoft.com/kb/218861