Create vector from scanned graphic

I need the design that's on some headed paper I've scanned as a JPG to be duplicated as a vector graphic... either Photoshop or Illustrator will do but Photoshop is preferred. It needs to be picture perfect and smooth (not grainy like the scan). It will need to be scaled to 925px wide and you will also need to extend the main background shape to span 1600px as it will be a website background and needs to look good on all monitor sizes. The font needs to be matched as close as possible.