What you want...is a standing rib roast. That is the cut. If you don't have a meat thermometer...get one because the inside temp will tell you the amount of doneness. It's pretty much fool proof...and omg wonderful.
It's a pricey cut of meat but you'll usually find it on sale closer to the holiday. Last year right before the 25th...I found them 1/2 off...I grabbed a couple to stick in the freezer.
Here's a link giving cooking times for various sizes.
Perfect Prime Rib, Roasted Prime Rib, Standing Rib Roast, Prime Rib Roasting Chart, Prime Rib Dinner, Yorkshire Pudding