After you file

Ditto.  For the federal tax return, you want pages 1-2 of form 1040 or 1040A. (Form 1040EZ is one page only.)  There is a signature space on the back.  For your state tax return, you want the pages of the main form (2 pages in some states, 4 pages in NY) that also has a signature space on the back.  It sounds like you don't need the other forms, schedules and attachments that some people have.

Download the PDF for "all forms and worksheets" and open it up, just print the pages you need, and sign them in ink.