My new rescue stinks

Hi everyone, I just rescued a beautiful tortie yesterday, and as she’s been getting used to our home, I’ve noticed that she REEKS. Her breath smells like garbage and her fur smells like a barn. She’s very skittish in the new environment but loves people, so she’s always trying to be directly in my face. I’m planning on taking her to the vet to see if she needs to get her teeth cleaned and I’m probably gonna buy her some dental treats (the shelter gave us a bag of science diet but I’m not sure if that helps with dental in cats). But is there anything I should do for her fur? Is the smell going to go away eventually now that she doesn’t live on the streets anymore, or should I try to give her a bath? Thank you