What is the best opening to quickly get out your rooks?

That's not how chess openings work (replace "rooks" with "queen" and see what you want is the first thing people advise beginners not to do).

The only undefended pieces at the start of the game are the rooks, and no one cares because they're that useless until mid to end game.

Every piece with a diagonal attack is an issue for a rook, and right at the start of the game is 8 pieces with a diagonal attack. 

just don't do it. you will get destroyed. there is no real way to get your rooks early. if h4 rh3, you get taken, and you lose rook for bishop, which might be okay in the opening, but good luck surviving the endgame. But if you really want to bring your rook out early, you can give up the center and tempo for something that is a little bit safe. Don't do this, but this is the best way if you insist.

another note: do not do this on the other side, because f3 g4 is fools mate. 

conclusion: don't bring your rooks out early. follow opening principles.

(edit): if anyone else can find a better way, feel free to correct me.

There is no point of getting rooks out quickly. They are the most powerful pieces after the queen, but thus they are also the most valuable and have to flee for all attacks.
The most important to develop rooks is to castle, so as to connect both rooks.
Sometimes a rook can be put into play without moving it. E.g. 1 e4 g6 2 h4 intending h5 is playable and makes Rh1 active without moving it.
The general rule is to develop pieces in ascending order of power and value: first 2 pawns to open diagonals for the bishops, then the knights, then the bishops, then castle to bring the king to safety and connect the rooks, last but not least fins a good square for the queen.

When I learned chess naively at school our first openings concerned bring the Rooks out early.

We quickly learned not to do this.

The fastest and the safest way to bring out your rook is in Budapest gambit

Benko Gambit maybe

of course there are a million other ways to play the benko gambit and i dont even know if im right about the rooks thing

Rooks are generally best on open files so if you are looking to get rooks out early perhaps consider openings that create open or semi open files early in the game rather than going for unnatural, premature rooklifts. One example of such an opening is the French Defence Exchange Variation where there is an open e file after move 3.

This is just one example. In addition it will probably take some time to develop the second rook. Nevertheless, keep looking there probably is some opening I don't know about that allows you to speedily develop both rooks to open files.

Rooks are an end game piece. They aren't ment to get out in the opening. Once they are out the area just a target. You should stick with some basic, popular openings, like the Vienna, or the kinds Indian.

neither of those are really "basic" openings though but i generally agree with your statement

1.d5 completely ruins this

Why would you want to do that? Oh, this might be a troll thread.

what if a3 a6 Ra2 e5 Ra1 agreed draw magnus-hikaru budapest 2013