I remember thinking a grapnel was a good idea; that changed on a halibut hunting trip, when I anchored (sand), dropped down, and was able to follow for about 200 yds. where the boat had been. It also dragged on occasion in rock, as well.
I now use a Danforth knock-off; seems to work well in just about every type of bottom I have to anchor in (rock, sand, and soft mud.) For windy days, make sure you've got enough chain. In rock, this system may be a problem in that it tends to hang up on occasion; if you're diving, it's not a problem - quick dive to clear it. A trip line may help with this. You want somewhere from 3 to 8 times the depth you anchor in as a rode.
As far as lines, it depends on where you're going to be, and how you're going to be securing the boat. I have about 12-15 feet on each corner for tying up to docks (you could get away with 2, and move them as req'd), along with a couple of flat fenders for longer stays (couple of hours max.) Should have a decent length of fairly heavy polypropylene, should the need to tow or be towed arise (try to stay away from nylon, if possible.) I will defer to anyone who has opinions about what's needed in slips, as I never slip my boat.