Hi, welcome to TCS and bless you for adopting from the shelter. Your girl is gorgeous. She looks like a domestic shorthaired (DSH). Usually red cats are male; I think the odds of a red female are something like 1 in 1,000. (Someone please correct me if I'm wrong on this.)
Domestic Shorthair cat. Some people call the color red while others call it orange. The diplomatic answer is you have a butterball kitty. I adore butterballs as they have such lovely colors including their soft pink pads. Your kitty is beautiful.