Getting Into Management Consulting as a Recent Graduate

As a recent college graduate I have been exploring options within the consulting profession (mainly management and strategy consulting). I have a few questions about the profession, and how to get my foot in the door. Before I start a few details about my situation:

-I graduated from Bentley University (a well known business school in the Boston area) this past May, with a B.S. in Information Systems Audit & Control.
-I am currently taking courses full-time to receive my MBA (from Providence College) next May (2018).
-I have a job offer to work at a regional accounting firm in the New England region (clients all over New England). The firm is growing and gaining recognition in the New England area. I would be either working in audit or tax (my choice).

So, I have a few questions:

-I understand it is extremely difficult to get into the consulting profession as a recent graduate, especially without a MBA from a M7 school. How difficult would it be with my background? Also, are there any specific mid-level firms I should look at when applying? My heart is not set on only the major firms, I really just want to get my foot in the door and gain experience.

-Assuming I am unable to receive an offer for consulting, what other positions should I apply to? Business development, strategic positions, etc.? Keep in mind I am looking for a position that would eventually set me up to work in the consulting profession.

-Lastly, if I do decide to accept the offer at the accounting firm, would the experience from that firm after a couple of years make me qualified for a position in management or strategy consulting?

For anyone who has taken the time to read this all, thank you. I am sure everyone can understand the confusion and stress of deciding on a first job out of college. I want to make sure I go down a good path from the beginning.

Any advice is welcome!