If you are at a fhu site, then you can leave your grey open if you desire. I prefer to hook it , keep my drain valve closed and just open and drain as needed. Never leave your black tank open. You want to keep at least a couple gallons of water in your black tank at all times to help prevent the dreaded stone mountain from forming. I try to get it @ least 2/3 full before dumping (you may need to run water into it to accomplish this.) This will help with draining. We also flush ours out really well after each use (a clear elbow on the sewer hose will help you see when this is accomplished.) I also use the Geo method
to maintain my black tank. You do not need rv specific toilet paper, single ply septic safe like angel soft is ok to use.
For fresh water, I keep a minimal amount in there for bathroom breaks on the road. I hook up to city water at the campground.
If you are partial hookup then water conservation is key for your grey tank or you can get a honey wagon/blue tote to empty grey into. Some state parks may have limited water hook ups so you may opt to fill your water tank there or at home for that. I keep a y connector to hook two water hoses up in case I have to share a tap with someone. I also use a water pressure regulator to keep from having too much pressure in the lines (approxinately $8 @ Wal-Mart I believe).
Remember you want the white fresh water hose for drinking water and a separate hose for flushing your black tank.