I sought out a Master's before applying to doctoral programs. I did not apply to doctoral programs out of undergraduate because I lacked many of the upper division courses required and had no research experience. I also wasn't sure if doing Ph.D. was right for me at the time, or what field I wanted to go in to.
I did a Master's program in southern California, and three years later I applied and got in to eight of the fifteen schools I applied to. While this route was right for me, I'm not sure I'd advise it to everyone. Looking back, I think I probably could have gotten into a few programs the year after I finished my undergraduate program had I applied at the time. I also did two internships in national labs just before and during my Master's program that really strengthened my application.
Getting a Master's will set you back 2-3 years. For every program I got into, I was required to jump through hoops to avoid re-taking courses. Some of these were just passing the qualifier, but others were more intense.
I TA'd and relied on financial aid, and ended up about 60K in debt after three years. In San Francisco (as well as in southern California) living will be expensive. I don't know if you get a tuition waiver if you TA at SFSU, I did not at my Master's program. This required me to TA/GA 2-3 courses a semester in addition to taking and working on research, and I still ended up in a lot of debt.
I also could not do the exact research I was interested in through my Master's program, not even in the same field. Before deciding, I would first try to visit and meet with professors and find out who is actually taking students. Also find out where previous students in the Master's program have gone to for doctoral programs. If you visit, also meet current Master's students and try to find out what they think of the program.
For me I think the Master's program made sense, but I'm not sure I would recommend it unless you are deficient in research, courses, or GPA. Even if you have a low GPA and improve it in your Master's program, Ph.D. schools will still look at your undergraduate GPA. Some of them will care that you did a Master's and showed improvement, others will not.
Either way you're going to have to re-take the PGRE. I think you'd have more time to study for it working a full-time job/research rather than while being enrolled in a Master's program. It sucks, and is intimidating, but if you put in the time you will get a good score. From just understanding all the questions on the practice tests and memorizing formulas I think you can get above an 800 easily.
So now, in response to your specific questions:
- It depends from school to school whether getting a Master's makes you more desirable. I don't think it would hurt. It gives you a chance to show your dedication, gain research experience, and get some good recommendations. I think that's more important than the degree itself. It may be possible to get these doing unpaid research. One other thing that may be of benefit is the connections the professors at SFSU may have.
- I have found no preference for Master's students over those straight out of undergraduate. Again, I think it's more about the experience you gain (also presentations, publications, connections) that can make you more desirable. But this depends on how much work you put in, if you do the bare minimum to succeed in your Master's program you probably will not get into any Ph.D. programs when you apply again.
- It varies from school to school. I am hoping to shave a year off my doctoral program, at the cost of three years in a Master's program. I could have finished in two, but I really wanted to take electives in areas that interested me and do a more thorough job on my Master's thesis. But when I was making the decision to finish in three years I was still uncertain whether I wanted to apply to Ph.D. programs. I started research at the end of my first year in my Master's program (June), so I really only had a few months to decide after starting research whether I wanted to apply in the fall or wait for the following year.
If you have additional questions feel free to ask them or message me. I don't know all of the details about your situation so I can't say what is the best decision for you. Are you applying straight out of undergraduate? Is the research you could be doing next year in a field you're interested in? What was weak on your application this time around? Did your mentor write you a recommendation for this round of applications? If you took a year off and did research, would that make you a more competitive applicant next time? Did you apply to too many prestigious schools?
If you are applying straight out of undergraduate, you could apply for SULI internships for next year. They are a semester long, and you can apply up to one year after you graduate. I believe your application is good for one year as well, so you can potentially apply for the fall, spring, and summer. I think this research and the connections I made doing it were another thing that really helped strengthen my application.
Good luck deciding!