Newbie questions: What kind of pet carrier?

[A very sweet stray or runaway cat has adopted us and we, ignorant of
all cat issues, are in panic. That's why I have a few posts each with a
question.]

First, we want to take her to a vet (Chicago area). She seems to have
no problems, just basic check up and shots. (She spends several hours
outdoors each day.)

What kind of pet carrier should I get that would be good for this
purpose as well as longer drives we may have to take later. In
particular, soft or hard? What kind do you use?