To promote more lactic (creamy acid) as opposed to acidic (vinegary), two things help promote it. Higher hydration and warmer temperatures. Likewise, colder temps and lower hydrations promote acidic acids. Lots of bakeries make the dough and then proof the dough overnight in retarding units. The retarding promotes the acidic acid, which leads to the sourness that most people THINK they want. Most bakers, however, think the acidic acid masks the true flavor of the wheat.
At the risk of sounding like a geek, it's a little more complicated than that. Granted, the whole "high hydration/warm temp" fermentation has become a fairly widely adopted rule-of-thumb in sourdough-baking.
Carefully controlled temperature and feeding regimen can also bias the population dynamics of the culture in favor of yeast (although they will still be outnumbered by lactobacilli by at least 100:1) which is why IMHO, if you want a milder tasting sourdough, I'd recommend feeding with greater frequency and with higher inoculation (not necessarily your storage starter but whatever portion you've set aside for making dough).
Higher hydration and warmer temperature are favoured by bacteria period. Lactic acid is pretty much guaranteed as a product of any sourdough fermentation. However, there's no DIRECT correlation between hydration/temperature and ratio of lactic/acetic products. Without getting too far into it, there are
lactobacilli which ferment and produce lactic acid only and those which ferment, producing lactic acid AND acetic acid (or ethanol) (and some which switch behavior depending on conditions!). Substrate (and co-substrates: fructose in particular) is the key factor - more so than hydration or temperature. Hydration and temperature affect, among other things, enzymatic activity and thus availability of substrate. Mentioning rye for a moment, with its pentosans (and thus a source of pentoses), which can have a big impact on the heterofermentative pathway (in this case fermenting 5 carbon sugar producing acetic acid or ethanol* in addition to lactic acid).
While acetic acid in high concentration may well overpower the "true flavor of wheat", it is also a volatile acid (unlike lactic acid) and it has been proposed that in smaller concentrations can be conducive to more complex flavor/aroma in the final result (as can ethanol). Lactic acid, on the other hand, is just "sour" (acidic)...although less stringent than acetic. Personally, I dislike overly-lactic starters/doughs but that's more an issue of taste than anything.
Side Note: When a starter has been left to to ferment too long, the "nail varnish remover" odour one might detect is a result of the esterification of acetic acid with ethanol: ethyl acetate, the same substance found in some glues and nail polish removers.
All that waffle aside, there is no (easy) way of knowing for sure which lactobacilli (or other LAB) and strains of yeast you have in your cultures. Getting familiar with how the starter responds to feeding etc. is very much a hands-on affair. Finding the optimum regimen for your particular culture is, at least partly, a matter of experimentatio and, of course, taste.
*I may be wrong about the details of pentose fermentation. I vaguely recall reading there being some reason why one product (acetic or ethanol) occurred to the exclusion of the other...but I might also be imagining it....if so I apologise!