Obviously metric, since that's what most of the world uses abd you're cutting yourself from a large chunk of your potential audience. The cholesterol measures are already metric.
The site is going to be limited to the US anyway. The data is calculated from a US population for US lifestyles. And the racial information is US-centric. Does 'Asian' mean Korean, Indian, or Palestinian? Is an African African-American? Even if they're Moroccan? The medical term for that genotype is 'negro', but that word has far too much baggage to be used with a primarily US audience.
And making the units even more alien doesn't help when you have to look them up and after an exhausting search find out they are imperial/metric and have to convert further.
Well I certainly know one of two bits of information this app can use to make its guess but I still can't use it because.. well.. you know. Defeats the purpose altogether.
For height/weight, I'd assume meters and kg?
When you get your cholesterol measurements, do use mg/dL, mmol/L, or something else? What about blood pressure?