What is the best opening for white? What's the best defense for black

For white, Queen's pawn up 2 spaces. For black, King's pawn up 1 space followed by Queen's pawn up 2 spaces.

There cannot be the best opening objectively. There are sound and unsound openings. The rest depends on your taste. You choose an opening which is easier for you to use and understand.

As Eugen said, there really is no "best".
If you want to go merely on statistics, 1.d4 scores 56% for White in databases, more than any other first move.
Black depends on your objective. Are you looking for the highest percentage score all told, which would be the Sicilian, or the lowest percentage of losses, in which case 1...e5 is the best move? Overall score and lowest losing percentage are not the same thing. For example, 2 wins, 14 draws, and 4 losses is a lower score than 7 wins, 5 draws, and 8 losses (by half a point), but you lose fewer games that way.

I play the Sokolsky Opening and 1 e4 as white. Against 1 e4 I play the Pirc Defense and against 1 d4 I play the Nimzo-Indian Defense. I also play the Modern Defense against pretty much anything.
As an adult learner with limited time and a lofty goal, the best opening repertoire for me is one that is relatively simple to learn and maintain, gets me through the opening on equal footing and to positions with which I am familiar and know the plans for. You can read more about this approach in this post on my blog.
http://becomingachessmaster.com/2015/03/22/my-chess-study-plan-opening-study/

That's a bit weird
ThrillerFan wrote:
Murgen wrote:
It depends on the opponent! ;)
Against Murgen - 1.b4!

White: 1.e4
Black: 1.c6 (against 1.e4) 1...d5 (against 1.d4) 1...c5 (against 1.c4), {input sensible move here} (against anything else)

e4 is the best opening but you should select depending on your skills.also before playing any opening you should know that opening in detail plus you should have knowledge of 2-3 more opening becoz every time new position will be there.and you can not say this is better or this ...everything depends on your knowledge and your opponents knowledge (response).so before selecting any opening, understand it first.