use the best grease you can, ideally waterproof with corrosion inhibitors.
When adjusting the bearings, do bear in mind that the QR will compress a hollow axle somewhat when it is tightened, and this affects the bearing clearances.
The correct adjustment is (with locknuts tight) a little free play that just disappears as the QR is tightened.
For cones etc you ought to be able to order them from
- any shimano stockist
- several of the large german retailers
- SJS have stocks of many of the more common parts
You can find the correct part numbers by finding the 'EV techdoc' for your model shimano hub. Once you have the full part number, try googling it in order to identify suppliers.
However because of the way that these part numbers work/are listed, it is worth trying
a) without the first and last digits to the part number and/or
b) with different punctuation in the middle, i.e. with space, or with hyphen, or without either.
cheers