What are My Internships Really Worth?

I'm gonna try and make this quick so I don't bore anybody. Basically I just have a few questions about entering the IB world based on my current experience.

I'll start off with a little bit about myself. My ultimate goal is to get into IB after undergrad and eventually move into Hedge Funds and maybe even start my own firm someday. In the Fall I will be starting my second year at Fordham University with a major in Finance. During Freshman year I had an internship at a local Accounting firm through a family connection. I am now thinking about getting into some other type of internship during the school year and next Summer. I was thinking maybe a PWM firm or some local investment office.

Basically my questions are:

Will this internship at a local no-name accounting firm help me at all with breaking into IB?

If I can get an internship with a local trading/investment firm or brokerage will this be helpful?

When/ how do I go about shooting for the real internships at the BB banks?

Will having these experiences at the smaller firms help me land bigger and better internships/jobs?