I would say it depends on which color you are, but I am no expert by any means.
Which is better, e4 or d4? (or c4?)

Those moves are obviously for white since, when playing by standard chess rules, black can never make it to Any4 on the first turn. 1. e4 is good, but 1... e4 isn't.
I'm surprised there are not any more comments. These "What pawn should I move first" questions seem explode with comments. I think before anyone can answer this question, the person asking it should first be asked "What for," since these openings tend to lead to very different play. It's kind of like asking:
What's better?
Mr. Clean?
Bon Ami?
Toothpaste?

C4 is a flank attack if i remember correctly. A player must learn to play e4 or d4 before learning something like this b3 , b4 , c4 , f4 etc.

Until I've memorised every variation of every line I wouldn't like to comment.
I hope you meant understanding every varation not memorizing

Until I've memorised every variation of every line I wouldn't like to comment.
I hope you meant understanding every varation not memorizing
Na, memorizing, it should keep me busy.

Until I've memorised every variation of every line I wouldn't like to comment.
I hope you meant understanding every varation not memorizing
Na, memorizing, it should keep me busy.
Are you sure you can memorize every variation?

I prefer playing e4 but I sometimes play d4. I don't like openning the diagonal to the King. I also don't like playing against d4 as much simply because I'm less familiar with it.
e4 is generally going to give you a tactical game, but there are much more lines that you have to know (sicilian, french, caro, scandinavian, whatever you intend to do if he plays symmetrically).
d4/c4 is more likely to give you a positional game, and there are generally going to be less lines that you need to be familiar with. I've only faced dutch once, and KID about twice (although I transposed them into Pircs). Black's first move is pretty much going to be either d5 or Nf6, and his second move will probably be the other.
Although I like the tactical, suspenseful side of e4, I do NOT want to learn what to do against all the different defenses. So I play the Veresov (1.d4 Nf6 2. Nc3 d5--and those moves can happen in any order). If you play the Veresov, you pretty much only need to know the french and the veresov.
It really depends on what kind of game you want to play. e4 openings usually lead to an open game(files, ranks and diagnals open early in the game) which tend to be more tactical(when you bring your pawn to e4 it is unprotected and is a target for your opponent). d4 openings usually lead to a closed game which tend to be more of a positional game (as the pawn at d4 is protected your opponent has to use more than one piece to attack it). c4 openings is a flank opening where the player prefers to control the center with pieces instead of pawns.(usually a transitional game, where the game can easily transpose into an e4 or d4 type opening)
Like the topic's title implies, what is better?
1.e4?
1d4?
1.c4?