You never get a second chance to make a first impression. When the time comes for that first impression, you take the time to be extra presentable and impressionable: clean clothes, fresh copies of handouts, research beforehand.
What first impression does your e-mail present; not the content, but the e-mail address itself? Is your address “yourname@yourpersonaldomainname”? Is it “yourname@ yourcompanyname” ? Or, is it “somecrypticglop@somefreee-mailsite”?
What goes to the right of the “@” speaks volumes about you, your profession and your success. “email@example.com” and “firstname.lastname@example.org” convey a more professional and successful impression versus “ email@example.com”.
Free e-mail is great: it’s free! However, every time it’s used, that is what is conveyed. That’s fine if you are a student or need a personal account, which, again, is what your free e-mail account conveys. As a professional speaker broadening your horizons and clientele, you need something better. Get it. You get what you pay for.