All this stuff I read about PUA and obviously the main purpose is to get laid with the hotties you see but to be honest whilst I agree that would be nice, I would personally see the main purpose IMHO as being approaching random cuties and hopefully passing through to the mid-game and number closing with the real aim of being JUST FRIENDS.
You know, just good social company to meet again for a coffee or day out and be like brother and sister really. Any further progression towards proper holding hands and kissing and sleeping would only be one of those natural progression things that either does happen or does not and between mutual consenting adults only. But I do not see getting laid as the be all and end all.

So - in a nutshell - I am entering the game as more of a social circle expansion thing than a big dating thing. which leaves me asking two questions:-

1) Have I just made a complete mega contradiction of the whole scene and am I wasting my time?

2) If not, what good ways are there of approaching girls WITHOUT them thinking anything along the lines of "Oh no, he is chatting me up".

I chat up every girl I meet using things I've learned from PUAs. Just because you're building attraction in a woman doesn't mean you have to act on it. Almost all of my female friends are girls who I've practiced gaming on who hang out with me because I'm cool. If you don't want to f close, then don't f close.