I worked as an editor in college textbook publishing for 20 years and didn’t have an MFA in writing–I had a graduate degree in a totally unrelated field. I fell into the job; it was totally unplanned. As you probably know, the publishing industry is extremely competative. I’m not sure that an MFA will give you much of a boost over other applicants. That being said, if you really want to pursue an MFA, I would do it full-time and try to get into the highest ranked program.
Here’s a ranking of MFA Writing programs in the US with information about funding and post-grad placement. (http://www.pw.org/content/2011_mfa_rankings_the_top_fifty_0?cmnt_all=1) If I were in your position, I’d apply for one of these programs that offers funding and where the cost of living is low. You will probably have to take the GRE and will definitely need to provide writing samples.
Since your goal isn’t to be a writer, but to work in publishing, you might want to look into non-degree programs that focus on publishing. The publishing industry (both trade and academic) is primarily in NYC. If you went to a program in New York you would probably have more opportunities for networking after you finished. The Columbia School of Journalism has a 6-week publishing course (https://journalism.columbia.edu/columbia-publishing-course) and NYU has options as well (http://www.scps.nyu.edu/academics/departments/publishing.html). At the last company I worked for, we hired a woman who had a graduate degree in Publishing and Writing from Emerson College in Boston (9http://www.emerson.edu/writing-literature-publishing/publishing-writing). Boston doesn’t have as many job opportunities as NY, but it’s got more than many other cities.
Finally, 25 is not old for graduate school. Good luck!