I'm not an expert in this field, but I think you need to define for us the source of profit/edge embedded in your market making strategy and the option trading strategy being utilised in order reach an answer on which risks to manage.
Some examples that come to mind:
a) if you believe your system models volatility better than other market participants and as a consequence you buy/sell options that in your model are under/over priced then it likely follows that remaining delta neutral is your primary concern, with theta/gamma being increasingly of concern if your strategy utilises shorter dated options.
b) if you believe your system models long term direction of the underlying better than other market participants then you probably need to keep your delta within some range and try to either max or min vega depending on whether your strategy leaves you long or short volatility
c) if you are HFT market making intraday with profit arising from the bid/ask spread and rebates, then you probably want to keep all the greeks close to zero.
In the absence of a specific driver, then a classic size x probability risk approach seems reasonable, i.e. model the dollar risk arising from a given movement/probability in each greek then in the first instance manage the one generating the most risk.
Hopefully an expert chimes in and corrects me if necessary.