Hi Lucan,
Firstly, congratulations on receiving a funded offer! In speaking with friends at other programs, I know that this has been an abominable year to be applying to PhD programs. A lot of programs are facing stiff budget cuts, and thus they are slashing cohort sizes dramatically. Rutgers is a rather strong program, and they would not have extended an offer to you if they did not think that you would make an excellent fit for their program. The fact that you also liked the program is a good indication that Rutgers' instincts were correct. This being said, here are a couple of things that I would encourage you to keep in mind:
1.) Graduate school is a 5-6 year commitment. It is not simply a stepping-stone to becoming a professor. It is 6 years of your life -- 6 wonderful, enjoyable, stimulating years. Consequently, you want to be somewhere that makes you happy. Harvard may be Harvard, but some people are miserable for 6 years in Cambridge. You are not going to do your best work when you are unhappy on most days. Job placement is a relative statistic -- students are just as responsible for getting themselves jobs as professors are, and a program that is going to equip you well to be a teacher, that is going to give you the freedom and the environment (i.e. happiness factor) to do the best work you can do is the program where you want to end up.
2.) ONLY do the post-bac if your language preparation is lacking. If you think that another year of Greek and/or Latin would have earned you a few more acceptances, then a post-bac might be advisable. I know both Penn and Georgetown have had tremendous success in placing students into top grad programs, but I think it would be a waste of your time and money to enroll in a post-bac if you don't need it. An MA is another matter, especially if you were to receive a funded offer from Vanderbilt. I know Vandy has also had a lot of success placing candidates. If you don't get a funded offer, however, then I can't believe it would be worth it to go into debt for two years, only to be faced with the uncertainty of applying to PhD programs again.
3.) While this shouldn't necessarily be a deciding factor, I believe Rutgers is a program where you have to earn an MA before you get your PhD. As a result, you could always apply to transfer out after you get the MA. Obviously you don't want to enter into a program already thinking you are going to leave it, but you would have the potential flexibility to look elsewhere if you ultimately decided that Rutgers was not the ideal fit for you. Nevertheless, as somebody else pointed out, Rutgers participates in this amazing collaboration with Princeton, Columbia, CUNY, NYU, and others that would allow you to take classes at any of those programs. This means there is always an opportunity for you to establish relationships with professors at other programs -- professors who could ultimately be on your dissertation committee, and thus other professors who could write on your behalf when it comes time to apply for jobs.
So, go ahead and chat with Rutgers about job placement if that is your biggest anxiety. Talk to your current professors. Everybody will have their own opinion, but ultimately yours is the only one that matters. Remember that you do not have to make a commitment one way or another until April 15. Wait to hear back from Vanderbilt. And trust your gut. For what it's worth, I rolled the dice three years ago and turned down a fully funded program that was on par with Rutgers to do a funded Master's in the UK. I reapplied after completing the Master's, and I had my pick of programs. However, I turned down my initial offer because I wasn't sure the program I had been accepted into would be a good fit for me. If I had liked the program more, things might have turned out differently.
Good luck, and don't forget to bask in the glory of your acceptance. Once you start your PhD, it will be a little while before people are fawning all over you again.