I personally wouldn't put any more stock into the security of your cable provider than I would with something like GMail. In fact, I am far more skeptical of Comcast or whatever than I am of Google. Google actually has competition, and therefore cares about your security to a great extent. What they use your personal info for as far as targeting ads etc. is a separate issue, but their systems are rather secure in my experience. I haven't used my free ISP e-mail address on any account since I was with Earthlink (LOL) back in the late 90s.
I have been using GMail since the invite-only days, about 12 years ago with no incident. I have a separate account for anything that I have to register for online, and a separate account for personal and sensitive e-mail that is basically just an account that sees a lot less traffic and is less susceptible to spammers.
If you want something that is totally off the radar and permanent just to you, set up a domain name and get an e-mail account through it. I have been using iPower for my domain registrations for a decade now and have been really happy with them. Once you have a domain, you can set up unlimited e-mail boxes that no one is likely to ever have any desire or inclination to hack to read your mail. It's a really good system, and will cost you $16 per year for the peace of mind.
If you go that route, it's really easy to set up your accounts on your computer e-mail client like Outlook / Thunderbird / Mac mail, on your smart phone, or via the web on any computer.