The best response for 1.d4

I bet everybody who read this topic know the best and also the most popular responses for 1.d4:
1...d5 or 1...Nf6

I think both of these responses are good, but i wonder, what response is the better one?

To choose, i would present some moves forward, and that will help to decide, which position is the better for black.

I will start with 1...d5. I think the most played and the best move for white now is 2.c4, known as the queen's gambit. Now, the gambit could be accepted or declined. I will show some lines of those and we will look at the position. Let's start with accepted. the main line goes like this:

As you can see, white is more developed and preapers a castle in the king side. Maybe people like this position as black, but i really don't like to continue from here my game. Just for you to know, black's favorite response is c5, but we will not go into it.

Now we will look at what happenes when the gambit declined. There are to ways to decline the gambit, but i will look at the popular (and i think better of course) of the two, the slav defense. Let's look at the main line of slav:

From this position there are many continuations, and i think this is only one position from many in the slav defense. I think the 2...c6 move is more flexible and make posibility for many options to continue the game and make it an open and interesting game.

Now we can look at how goes the game with 1...Nf6.
If white learned well the book he will play of course c4.
This is a really flexible position and black can play many options here. We will see three moves that can be made by black right now.

The first move we will look at is 2...e6. This move leads us to two openings, the nimzo indian and the queen indian defense. Since Queen's indian defense is not such a played opening, i will show you the nimzo indian, the popular and played opening here. This opening leads us to this position usually:

This is also a realy flexible position and white and black have many continuations here.

Now, let's look on the budapest gambit. I don't really like to play it as black, and to be honest, i know this openign from theory only, i never actually played it. This opening is 2...e5 for black. I will show here also the main line, and we will take a look in the position on the board.

From this position black is maybe more develpoed, and the pawn at e5 is going to fall soon. Maybe it's not such a bad opening :).

The last move i want to talk about is 2...g6. I saw this move in one of the games of Gelfand vs Anand. This move's point is to bring the bishop to g7 square and control the longest diagonal for this bishop. The main line i know goes like this:

Here there are also some continuations for black. I think the best (and also what gelfand played) is the Grunfeld Defense (3...d5), which is bery agressive move. Some moves after the bishop will come to g7, and it is a good position for black.

I did a hard job here, i would be glad if you correct my mistakes (not grammar mistakes!) and if you have more lines to add or something important to say, write it in the comments.

(credit to me, and don't be to hard with me, i am only 13 years old )

As long as you stick to lines that are accepted as sound, the choice should be more a one of personal preference than one being better. The difference in style between a queen's gambit and a king's indian is enormous.

The best way to learn about an opening may be to study the ideas that happen in excellent games, one at a time, with plenty of time. Find games that impress you, and see if you can use the ideas some time. 

Actually i saw an analasys of the 12 games between anand and gelfand and 1.d4 played in almost all of them. In this match i saw many forms, either the indian defense or queen's gambit. I thought it would be interesting to know which move should be played in these games, and of course to know what move do you preafre according to your style of play.

one thing you didn't mention is that 1. ...nf6 can transpose to almost any defense to 1. d4 so you can use it to see which way your opponent is going to play before comitting yourself.

When I was first learning chess back in the 80's and early 90's, the Grandmasters (after 1.d4 Nf6 2.c4 g6 3.Nc3) almost never would play the Gruenfeld. (3....d5) It was all about the KID back then. (From what I understand they were too afraid of the mainline Gruenfeld, which Karpov had perfected.)

Today, I see almost none of the KID, and a lot of the Gruenfeld. And white players almost never use the mainline anymore. (4.cxd5 Nxd5 5.e4) 

Not sure why I'm typing this. Just confuses me is all.

Then just to understand, is your point is that KID is better then grunfeld?

Like another person said, it's a stylistic thing.  I play various lines of the Queen's Gambit and Nimzo-Indian, the more "classical" defenses to 1.d4, and leave the ...g6 lines for someone else.  I tend to crush Benoni, Benko, and Grunfeld players as White, so don't have a ton of respect for those defenses.  The King's Indian, which I played for a while, I respect, but really just isn't my cup of tea.  However, if you do take that route, a "MUST SEE" game is Schmid - Gligoric, Hamburg 1965.  Black's 28th move is just outright astonishing!

Also, in response to the original post, the assessments and differences between the various forms of the Queen's Gambit are inaccurate.  In the Queen's Gambit accepted, it's not all about what happens in 5 moves.  The idea is Black will play a6, b5, and c5 (not in that order), fienchetto what is normally his bad bishop in the Queen's Gambit, and looks to have a more free game, with better scope for all his pieces, that at the cost of relinquishing the center.  The Queen's Gambit Declined, Orthodox (2...e6) has the upside of maintaining the center with the strongpoint at d5, but the Light-Squared Bishop is hemmed in, and Black ends up with a bit of a space disadvantage.  It's almost like a "bear hug" effect, and Black has to avoid playing too passively as otherwise he'll be squeeze to death, like as if the King dies of suffocation.  The Slav also maintains the strongpoint at d5 at first, but it doesn't hem in the Bishop.  That said, a subsequent ...e6 without pulling the Bishop out leads to a sharp defense called the Semi-Slav.  The downside of the Semi-Slav is it's a lot of pawn moves, and White gets a lead in development and space.  The Slav, however, doesn't allow for Black to hold the strongpoint on d5.  Black will need to take on c4 before pulling the Bishop out (usually to f5).  The upside for Black is the Bishop is active.  It's still his bad bishop, however.  The downside is the resulting weaknesses on the light squares on the queenside (especially b7 and d5).  Many amateurs like to play a reversed London setup, but it doesn't work.  The problem with 1.d4 d5 2.c4 c6 3.Nf3 Nf6 4.Nc3 Bf5? is that 5.cxd5 cxd5 6.Qb3 puts too much pressure on b7 and d5, and Black has to undevelop with 6...Bc8 as any other move will give White too great of an advantage, even if it's not in the form of grabbing a pawn.  I've seen moves like ...b6 from Black, and then the King gets into a lot of trouble.  The last one is the Tarrasch Defense, which has the upside of free piece play unlike the Orthodox, maintains control of d5 unlike the Slav, and doesn't fall behind in development like the Queen's Gambit Accepted, but the big downside is that depending on what line White chooses to play, Black will normally deal with either an isolated d-pawn, or else doubled isolated c-pawns, the front one being a passed pawn on c4.  Then of course you have the complete garbage, like Albin's Counter-Gambit, Chigorin's Defense, the Baltic Defense, etc.

I think i still respect those defeneses. Even if you crush players that use there defenedes, if they would know how to continue the game wisley they could draw and even win, then i think you shoudn't hate or unrespect these defenses.