I'm not sure there's any really practical way to do this.
1. Format | Background is for Web pages only and applies to all pages (not
to mention that you can see the background only in Web Layout view).
2. Format | Background | Printed Watermark will also, by default, apply to
all pages. You may be able to get around it by inserting a "picture" that is
just a large colored object, then checking "Different first page" on the
Layout tab of Page Setup, then removing the watermark from the Header (from
page 2, View | Header and Footer, select the object, and press Delete).
3. You can also do this manually by enabling "Different first page" and
adding a page-sized grey AutoShape to the First Page Header.
In cases (2) and (3), however, the background *will* print unless you (a)
remove it before printing or (b) clear the check box for "Drawing objects"
on the Print tab of Tools | Options, which will not work if you have any
other objects in the drawing layer (including text boxes) that need to
print.
Why exactly are you trying to do this?
