Networking Approach

Hi, since it is that time of year I wanted to ask you all if this was a good networking approach. I compiled a list in excel of all the alumni from my HS and University at various banks and since I don't have most of their emails I will be using this approach

1. Connect on LinkedIn
2. Contact the alumni that have accepted invitation
3. Ask to connect in person or at the very least a phone call

Is this a good approach? Since, I attend a non-target and don't have the email addresses of the current bankers I will use Mailtester.com and hopefully get some responses. I will also contact bankers that have their information/emails listed on their company website. And finally I will contact high priority people (VPs and 3rd year associates) with the 15 emails I get with the linkedin premium account.

Is there anything I am missing? I am currently a rising junior and my school doesn't have OCR for any of banks. This summer I was able to secure an internship at a PWM firm (not BB) in a very small farm-town 3 hours outside of Chicago. Also, I am going to start with VPs then move to Associates and then move on to Analysts depending on the responses. Is it beneficial to connect with ex-banker (people that worked at BB then move to PE) ?

Thanks you