How to Word Emails Asking Someone to Put in a Good Word for Me

I'm about to start as a freshman at a semi-target in a major city in a few weeks, and I know I'll need to start looking for an internship soon next summer. I've been reaching out to people the last few months and have made a few connections at a BB (PWM & AM) and at a mid-size growth equity firm that has an office in the smaller city where I'm from. Per advice from a mentor, I've read the Rosembaum Pearl IB book, and I have more knowledge about IB/finance in general than any of the people I've networked with said they would expect me to know at my age, so I know that I am better qualified/prepared than most incoming freshmen would be.

For the BB, how do I go about asking to put in a good word for me (which I know would mean a lot since I'll only be a freshman and some of the internship apps specifically say they want sophomores)? I've read that something along the lines of "How can I best position myself to get an interview for this internship?" is a good place to start, or should I be more direct in addressing that although I am young I feel I can bring a lot to the table and so on

As for the growth equity firm, they do not have a structured online app process like the BBs, but the first time I spoke with my connection there he had mentioned that they usually only have sophomore interns but know they have had a freshman once or twice -- so would the best way to approach that be emailing saying why I feel qualified, highlighting my ambition/work ethic, and then asking who at the firm I could send my resume to for consideration? or would a more direct approach be better here?

Also not sure if this makes a difference, but I was my high school valedictorian, have a near-perfect SAT score, and am on a full college scholarship, all of which I have on my resume, so it makes it clear that I'm a motivated person.