I own a number of corkscrews including the "Rabbit", for approximately $30.00 to $45.00 ,but the "church key" above which I prefer is both simple and inexpensive.
Why do I like this one in particular?
1) It has a small knife to cut the foil (below the second flange of the bottle).
2) It has a two-step hinge to make the extraction of the cork easy and to protect the glass at the edge of the bottle mouth by avoiding undue pressure.
3) The pigtail, with its 2.5 inches length and silicone, helps to pierce the cork more readily.
All of this for $6.00-$9.00 at most wine stores.
Cheers - Jerry