A new paragraph should always begin with first a space is how I was taught.
The rule I learned was that a new paragraph should be indented, typically five spaces, one standard tab stop. Nowadays formatting rules for letters and much else allow for a "block" appearance to pages and both manuscripts and books often omit the indentation. One space seems hardly enough to notice. (Unless we're still talking at cross purposes you mean a line break when you say "space" instead of a single space
on a line.)
And yes, publishers still require manuscripts (which are properly typescripts or computer files these days) to be double-space and to have generous margins, and for exactly the same reason they always did. Books are still edited, just at they are still mostly read, on
paper, not on computer screens. (They get physically
revised on computers, but that's a different process.) Wide margins and spaces between lines given an editor room to insert comments and revision. Same reason galleys are delivered on large, uncut proof sheets, so the copy editor, editor and writer can make corrections. (In this age of declining standards of literacy many editors and authors spend much of their time restoring things mistakenly "corrected" by the copy editor and/or removing fresh errors introduced by that person.
)
Hollywood (and therefore worldwide) script standards are even more anal. Those of you who have been buying the script books might be interested to know that JMS does not type his scripts on an old manual typewriter, nor does he just like the look of fixed-pitch Courier 10 pt. type. Everything about a script page - the font, the size, the margins, what gets typed in ALL CAPS, what always gets centered, what never gets centered and exactly how far everything that gets indented gets indented have become standardized based on the conventions that were found to work for guys who
did pound out scripts on battered Remington manauls with fixed-space fonts. There are a number of competing script formatting programs designed to automate a lot of this stuff and relieve the writer of the mechanics of it all. (The best packages also do a lot of other tasks the professional writer needs to do with various degrees of automation, like turning out a "shooting script" where scenes are grouped together by set or location and performers required, which is how they'll be shot in order to save time and money, or producing a list of required sets or props, etc.)
Regards,
Joe