One thing I learned about baking cookies a long time ago: to get a softer cookie, lower the temperature of the oven and cook them a bit longer. A higher temperature and shorter cooking time makes them crispier.
I have also made cookies with vegetable shortening, but I sometimes find it more of a hassle than it's worth (since vegetable shortening is not something I use for anything else in my kitchen). However, the very best cookie recipe in the whole world that I've ever tried comes from the King Arthur Flour Cookbook, and it uses both vegetable shortening and butter. The cookies end up ever so slightly crisp on the outside, and soft and chewy on the inside. They're wonderful.