Ideal bank to exit from associate position to HF or PE?

Wise WSO, I'd really appreciate your help on this!

I haven't worked in finance before, but I'm fortunate to say that I've been lucky with good credentials and a relevant background that would make me an appealing HF and PE candidate (I just finished grad school, and was considering academia in math/econ). But first, most of my HF/PE friends suggest that I work at a bank for a year or two to build experience with modeling and valuation before going for HF/PE, given my nontraditional path. I don't care about prestige since I'm not applying to B-school, I'd just like to learn a bit as an associate and then jump to HF or PE. What banks would be ideal for this? I've heard suggestions to look at MM boutiques so I could get a broader experience rather than being a spreadsheet jockey and working insane hours at goldman or Citi, but how much do I lose out on my exit opps by sacrificing name? Any thoughts much appreciated!!