We have not yet defined the borders of your Hunting Grounds. It is up to the group if we want to start this Job in our Hunting Grounds (it need not stay there).
If the Job happens in your Hunting Grounds and is classed as 'Espionage' (your call) then you get +1d to all Gather Information rolls you make there.
If you start in your Hunting Grounds you get one additional Downtime Activity (of any type) for free. You will get this at the start, so can use it to set up anything you might want before the Engagement roll --usually you would launch straight into Engagement on the first job. You could use this Downtime Activity to research the best place to start, and then declare that it is within your Hunting Grounds (or pay for it).
Since Downtime is on the table, and you still have some Coin you can spend it to pay for additional Downtime Activities as per normal.
As a quirk of Nightmarket, you can always take an +1d to Acquire an Asset there, at the cost of 2 stress. This is in addition to Pushing yourself or Taking a Devil's Bargain.
Due to Second Story, if your Type of Plan is some form of 'clandestine infiltration' (your call), you would get +1d to your Engagement roll.
If referring to or asking about particular post here, link back to the relevant RP post so we can have some context.