Advice for speaking to banker's to try to break into the field?

I graduated last year from a non-target school and unfortunately only realized by fall of senior year that I wanted to do banking instead of law. This of course gave me little to no chance to break into the sector. I ended up getting a job at a consulting firm and my group fortunately specializes in working with HF and PE firms. My current game plan is to use the next few years to make connections while also studying my ass off to get into a top MBA program and hopefully come in as an Associate. I was speaking with a close family friend about this and they mentioned having some old friends who work as MD’s and Heads of at some Investment Banks and PE firms who they would reach out to on my behalf. I won’t delude myself into thinking I’ll be thrown a job at these banks after being out of school for a year with no real relevant experience, however I want these conversations to go as positively as possible so that they remember me in a few years’ time (and I do hold on to some hope that if I impress them they might be able to make something happen for me sooner than later). My question is what are some things that should look over and be prepared to speak about before having these conversations? My biggest concern is my technical knowledge because I’ve been out of school for a while now. I’m taking the financial modeling course on wallstreetprep to jog my memory but if there’s any quantitative or quantitative things that I should be ready to speak about I’d appreciate the advice.