Graduating Spring 2014. Should I pursue internship or full-time opportunity for the summer?

Hello everyone,
First post on here, not sure how much feed back I will receive, but I will give this a shot.

Situation:
-I will be graduating in Spring 2014.
-I have a 3.85 GPA
-Highly involved in student managed investment clubs and work with the department of finance at my university (have a lot of experience with dcf models, valuation models, Security Analysis, bloomberg certified)
-Have 3 internships: 1 for investment management in a community bank, 1 in a small boutique investment bank, and 1 assisting in the accounting department for a non-for profit
-I am studying for Series 7 and 66 and will be looking to get sponsored by a firm
-Lastly, I come from a non-target public university

Goals:
- I want to get into either Asset Management or Management Consulting
- For AM I would like: JP Morgan, GS, UBS, Citi, or BlackRok
- For Management Consulting I would like: McKinsey & Co, Bain & Co, PwC, or Deloitte Consulting

Although I have a strong GPA, involvement, and internships, I do realize that I have not had a brand name internship in my resume. I know most top firms recruit from their pool of interns so my question is:

Should I go for an internship in the summer immediately upon graduation, so I can go for a full-time offer after the internship

-OR-

Should I go straight for a full-time offer upon graduation. If so, will it be to my disadvantage that I did not intern with any of these firms? and how likely will it be for me to get recruited for full-time with no brand name internship on my resume?

All of your suggestions are highly appreciated. I know the difficulties of coming from a non-target school, so that is why I want to get all the feedback possible. Thanks everone