Maximizing My Physics Degree: Considering a Second Degree or Pursuing a PhD

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I am currently a physics major at a fairly small school, that is not know for its physics program. I got into better schools, but I chose this one due to financial reasons. I'm on track to graduate in the spring, and I'm a bit torn between a few options that I have.

I can easily finish a second degree. A math degree would only take me 1 extra semester and 3 courses during the summer, and a CS degree would take me 3 extra semesters (I'm on track to graduate early anyway). Would this be a good idea? I've heard lots of physics majors have a hard time getting a job after they complete their degree, would this be a good backup plan if academia doesn't work out?

My other option is to go for a PhD right away. I've been working with the same advisor for about 2 years now, and I really like my research. My advisor believes that if I were to stay with him for graduate school, I could finish my PhD quite quickly (his estimation is ~3 years for a masters+PhD). Other people have told me that it isn't a good idea to get an undergraduate degree and a graduate degree from the same school, and that I should apply to a more "prestigious" graduate school. How true is this? If my ultimate goal was to do research (university or industry) would it hurt me in the long run if I were to stay here for graduate school?

Feedback would be appreciated
 
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There are many risks involved in doing a PhD. One of the major issues (in my opinion) is that you have to find a research subject and an advisor who fit you well. If you change to another school, you run the risk of getting an advisor or a topic which could make you disinterested in research. Right now, you have an advisor/topic that you really like. So changing school is a considerable risk in my opinion.
On the other hand, a more prestigious school could give you more options down the road. And it might give you a different perspective on things if you switch schools.

It's up to you really. If it were my choice, I would stay in the school you're in now.
 
A math degree would probably be helpful although not essential if you're interested in further academic work in theoretical physics. A CS degree is probably overkill as just a few programming classes and spending some time on personal projects to demonstrate your skills will be enough to get a foot in local businesses on the computing side. You probably won't be getting a job at Google but hey they hire people with all kinds of weird backgrounds, a CS degree will probably not make a difference.

In either case just taking a handful of extra courses for a minor would probably be sufficient anyway.