If you are using a font with letters that take up variable amounts of space, a single space after a period is enough. If you are using a typewriter or a monospace font, two spaces are better. Either way, a single space should follow every comma, semicolon, and colon. Underline text only if you cannot italicize it. It may look tidy, but it creates gaps between words that make reading hard.
Most word processors can kick such paragraphs onto the next page.
This may create huge lower margins, but it's better than breaking a paragraph. Be sure that each page displays a plain Arabic numeral in the upper right-hand corner. Otherwise, don't bother with a header. They're not going to scatter your ms. or lose the title page. And when you send it in, don't bind it in a cute cover.