First, as to gratin dishes. You don't want to make one large potato pie, you want a small-ish dish for each person. I started making these in small dishes when people complained that others were getting all the brown crusty edges and it was not fair. So when there was a sale at Crate &Barrel, I picked up one small ceramic baking dish per person and one for the house. The important thing is the dishes must be able to go in the oven, and they need to be about 1 inch to 1 1/16 inches deep. Mine are about 6 inches by 7 inches.
Next, as to potatoes. I've had the best luck with Idaho Russets, and I recommend them.
Turn the oven on to 400^. Put the empty gratin dishes onto a baking sheet, put a slice of butter in each dish, and put into the oven to let the butter melt.
Peel the potatoes, rinse and dry. For 4 gratin dishes, I used 2 medium-large Idahos.
Heat the cream and half&half in a heatproof pitcher or a little pot that pours easily. I used a cup of half&half and a generous half-cup of heavy cream. Heat it until it's very hot but not boiling.
Remove the baking sheet and dishes from the oven, and swish the melted butter around each baking dish and up the sides.
Now, one at a time, cut a potato in half the long way, and cut each half in half the short way. I slice mine in a Cuisinart food processor using the 2 mm blade. I've also used a sharp knife. Either way, you'll wind up with a few stacks of half-moon-shaped potato slices. Pick up a stack, put it into one of the baking dishes, straight cut side down.Give the stack a little push to spread it out around the edge of the dish, using additional stacks as needed to fill the dish. Fill each dish with potato slices, peeling and slicing more potatoes as necessary. You'll be working from the outside in, and if there's an empty space in the middle of a dish, fill it with small pieces of potato. This would be a good time to grate a little Parmesan or Swiss cheese over the potatoes, if you like. Not mandatory.
Now pour the cream mixture into the dishes, trying to keep things even, and using the baking sheet, put the whole assembly into the oven.
Baking time will vary because potatoes may have different moisture/starch content at depending on time of year, how they were stored, etc. Start checking after 30 minutes, mine usually take about 40 to 45 minutes. Ovens vary, too.