Which are more selective for trading applicants BB/HF/Prop shops?

It depends completely on which ones you are talking about. They also select for different things, although virtually all of the elite firms though recruit from a very short list of schools, which includes only a few non-elite schools and those are mostly only because of proximity (ie UIllinois/UWisconsin for trading jobs in Chicago or NYU in NYC). Very few actually look at any resumes emailed to them either and focus almost exclusively on the few schools where they do OCR.

Hedge funds>>>>>>commercial banks (you mean BB's? for prop or sales trading? way different)>>>>>>>>>>>>>>>>>>>>>>>>>>>>>wendy's drive through>>>>>>>>>>>>>>>>>>> ihop waitress>>>>>>>>>>>>>>>>>>> prop shops you mentioned

I fail to see how the answer to this question will in any way affect your life.

Yeah really. I would bust a nut if any of those firms wanted to hire me as a trader.

If those firms are not doing OCR at your school and/or you do not have some kind of connection to one of those firms, you are not getting a spot, pretty simple. TBH, you should do a lot more research on what you 'want' to do because there is very little similarity between that list of shops. I mean shit, you have everything from global macro HF to prop HF/algorithmic trading to market-making and everything in between. The types of candidates each of those places is looking for is very different.

Also, where did you even get the idea these places take ppl straight from undergrad? I mean sure, they have taken a limited number in the past and I imagine they will continue to take them into the future, but it is a tiny number and they generally already have great experience (and connections). On top of that, if you're @ Tudor or BWater, you're going to be an execution trader and not on the way to PM and if you're @ JSC, you're more likely to be doing algorithmic development and programming than actual 'trading' per se.

What I meant by my original question is one firm more difficult to get in than the other if I am applying as a non-conventional applicant (hotshot connections only - academic background a disaster other than famous prep school). I am a very crappy writer so I will say this: my only shot at becoming a professional trader is though big deal connections I have who might ask their friends on the Street to help me, that sort of thing.