If I want to play KIA then should I start with 1.e4 or 1.Nf3

If you like plans involving f2-f4 rather than h2-h4, then I suggest you go 1. e4 and employ a variety of systems. For example, you could play the Vienna with 3. g3 against 1. e4 e5 (or with 3. Bc4 if you prefer) and the Closed Sicilian, but play the KIA against the French or Caro-Kann. The only lines which might cause a problem are the Scandinavian, Pirc or Alekhine. You would probably have to learn some different systems against them, but it's nice to play a variety of positions in your games.

I've been told it doesn't make sense to play it against the sicilian, but I don't know. 

Fischer used to play it against the French and against the ... e6 Sicilian.

So then wait until move 3 to use it against the sicilian? 

Fischer sometimes used the line 1. e4 c5 2. Nf3 e6 3. d3 heading into the KIA, yes.

I seem to recall a game vs Ivkov...

EDIT: Yes, here it is: http://www.chessgames.com/perl/chessgame?gid=1044241

hi, i think white should only put bishop to f4 when pawn is seriously threatend, the bishop is also good at c1!
i wrote 2 articles about the kia, the first one deals with its history, the second one with one of fischers best games

https://improveinchess.wordpress.com/2017/08/30/how-to-learn-openings-kings-indian-attack/

https://improveinchess.wordpress.com/2017/09/05/how-to-learn-openings-2-kings-indian-attack

Depends. If Black has played Qc7 (a very common post for the Queen) then White's Bf4 threatens Nbd2-f1-e3xd5! and after exd5 White pushes e5-e6, threatening both the Black Queen (with the discovered attack by the f4 Bishop) and the d7 Knight (with the Pawn itself).

when Qc7 is played, the knight should be on f1 already, then i go for h2-g4 and maybe Nf6+!