“I am currently unemployed, but will graduate this Fall with MS in Accounting.”
Great, then you'll still have fall recruiting & career fairs. Also, I wouldn't consider you unemployed, I'd consider you to be just a full-time student.
“I want to begin my accounting career working in an accounting firm (preferably public, even more preferably top 10 or big 4), so I am applying to every accounting firm job I see get posted, in the hopes that someone will take me.”
Definitely utilize your on-campus resources. In my experience applying to campus postings have much higher success than applying via online to company's job ads.
“This will add up to a hell of a lot of applications. Figure around 20-25 firms, all of which post 2-4 different job/internship opportunities.”
Once again, focus on the firms that recruit at your school and apply thru your college's joblink website whenever possible. Also, do not apply to multiple different positions at the same firm (it shows that you don't know what you really want – and then they'll ignore all of your applications). Just pick one opening at each.
“However, I am worried that I still could get passed over by everyone.”
Try not to get too stressed out with the process. It takes time and everything will work out okay. Remember, a lot of majors don't even end up looking for work until after graduating – so you already have a head start. As long as you keep at it and are smart about it, you'll definitely have something at least by 6 months after graduating (which is better than can be said for many).
“In that case, I would still need to work. For that reason, I am starting to wonder if I should be applying to random corporate accounting jobs/internships as well.”
Yes, once the fall term starts, go to your schools career fair, check out company open houses/events in your nearest big city, browse those big company's postings located in your area.
“What holds me back is that I might not be able to take off work to go interview for better (cpa firm type) jobs if they start me working right now, and that I will have less opportunity down the line.”
This is shady as shit. Don't plan on accepting an industry job to just then apply for public jobs. First of all, you should only be looking at jobs with start dates after you graduate. Secondly, you should only accept if you can see yourself working there for at least a year (which may be the length of time for you to really figure out how you feel about it). Also, generally those fortune 500 entry level jobs pay better than the ‘better cpa firm type' jobs – and many of them have growth opportunities just as good as public accounting.
“Should I hold out until I get the right job? Or just start working wherever (corporate).”
Just to be clear – public does not equal right. So yes, try to hold out for a good position at a good company – but also be open to new experiences. You are so very laser focused on public accounting, no doubt you are missing out on some fantastic opportunities that pay better and offer better opportunity.
“I am not about to go broke and can hold on without a job at least until January. Is this smart?”
Not sure what you are saying, You are saying you gradate in Fall (and fall term usually ends in December) and that you need a job ASAP in January. No that's bad planning on your part. Keep in mind, depending on when you are able to get an offer as well as the needed start date of that offer, you may have to get a ‘college student' type job in the meantime to pay monthly expenses. As long as your career job starts before your student loan payments begin, you should be fine.
“If your GPA is decent and you have any kind of interview skills there will be a public accounting firm that will want you somewhere.”
This is not my experience at all. I graduated from a great master of accounting program (with all good to fantastic students) and there were many that had their hearts set on public (due to the campus recruiting propaganda) and didn't get any offers. I think it really depends on your school and how competitive your area/state is. A lot of great corporate gigs hire in the fall, so I'd definitely encourage students to look into those during fall recruiting as well.
And if you don't get an offer right away, it is not because your interview skills suck – it's just very competitive out there. Don't stress too much and keep at it, things will work out.