With regards to bankroll, it comes down to a few things, namely your tolerated risk of ruin and your game selection.
If you don't mind losing your br, then you can obviously play on less and less buyins. If you're adverse to it and want the probability of busting to be as small as can be, then obviously you need a significantly bigger BR.
Game selection affects winrate and the variance encountered. Big edge against passive fish = high winrate and low standard deviation. Small edge against aggro reg = small winrate and high standard deviation.
Play around with the tool on the right hand side of this page to get an idea of how much you'll need.
http://www.evplusplus.com/poker_tools/risk_of_ruin/
Starting out at HU cash, whatever you do, don't over-estimate your winrate and don't underestimate the standard deviation.