Good question. I should have been more clear. For your bottles you are carbonating naturally, which requires some kind of sugar. My response assumed you would naturally carbonate the whole batch. In that case there is a correct amount of sugar to naturally carbonate the entire batch whether in the bottles or kegs. Most people that have a kegging system like to force carbonate their beer that is in a keg with co2. But the 16 gram cartridges don't have enough gas to carbonate the beer and then dispense it. If all you have is the cartridges, then I would mix the appropriate amount of bottling sugar for the entire batch. Fill the keg(s) and bottles then store all the beer someplace around 68 degrees. You don't want it cold because the remaining yeast will need to get active again and consume the sugar you added. This method requires more patience because you'll need to let it sit for at least a couple of weeks. When the keg is carbonated then put it in the fridge and use the co2 cartridge to dispense it.
When you fill your keg, you will want to purge any air that's in it. Just give the sealed keg a squirt of co2 with whatever system you have, then pull the relief valve, then repeat another 1 or 2 times.
If you have the co2 tank, typically 5#, and regulator, you can put the keg in the fridge, set the gas around 12-14 psi, and in a week it'll be ready to drink. No bottling sugar needed.
