Staying Put vs. Jumping Around?

A little background about me first:

• Did horribly in High School (graduated with a 2.25 GPA)
• Accepted into a no-name college where I worked my ass off, became the President/Chairman of every career-related on-campus organization that I could, founded a student managed investment fund, graduated SCL (3.85 GPA)
• Internship experience in corporate development, and now I am working at a boutique bank in the US as a graduate program student (will be promoted to ER associate next month)
• Taking CFA I in mid-July, already finished all ER licensing exams

Here's my question:

My dream (like half of you) is to break into an AM or HF in the next couple years. Is it better to stay put where I am currently (will be covering my own stocks within the next 1-1.5 years), or bounce to a BB firm in ER?

Also considering an MBA down the road if I have no progress with the buy-side job search. Is it better to have the BB name on my resume, or have the single work experience mentioned above when it comes to getting into an elite MBA? Also is the no-name school going to put me out of the running for an elite MBA?

Thanks all,

MD