Most secure email account for RVing & traveling

The best one is the one I use. Gmail. hehe

I'm not real sure what you mean by secure email. It's the internet connection itself most people get concerned about.

I second G-Mail. I think Google is way ahead of the competition in terms of security of passwords, user names, etc.
I use two step verification when logging into Google. Makes it very hard for the bad guys to steal my info.

No matter what people say don't put any info on any email account you don't want made public. Only safe internet is "https".

Well truth be told, if you use Gmail you'll see the "https". And on Hotmail, oops excuse me, Outlook.com now. I would imagine Yahoo too, but don't use it often enough to know.

In the last few days there have been a number of news stories about hackers stealing the user ids and passwords for five million gmail accounts.

You can check to see if yours has been stolen at this web site.

https connections or two step verification make no difference, because the Russians have been stealing the userids and passwords by hacking into the Google gmail servers directly.

The safest email approach would be to establish your own email server on the internet used only by you. Of course you would make it as secure as you can, but the real security would be that since it only has one user, it would not be worth the hackers time and effort to go after such a small fish. Their efforts got them five million gmail accounts, why should they waste time trying to get yours. They would probably never even recognize it was out there on the internet among the millions of other servers.

I'd go with either GMail or Outlook.com. Both use SSL sessions, and also have better spam and Malware scanning on the server end.

Most hacks are due to using a too obvious password, or by Malware you may have inadvertently installed thinking it was something else, or part of another hacked software. You can take steps to prevent this.

Other email accounts are exploited not by obtaining the account password, but by extracting the session credentials due to server vulnerabilities. Not much you can do about this on your end.

Using your own domain name virtual web hosting may not be much safer. The server admin can access your account and intercept/read your emails.

Have a old PC and decent Net connection? It is possible to setup your own Free LAMP server, SSL certificate, email server software, and possibly use a DNS service, but way beyond the technical knowledge of the vast majority of email users?

They are all the same. They are all both good and bad. If you thought your CC was safe at Target or Home Depot you have recently been surprised.
I consider e-mail an open form of communications much like my phone line or cell phone.
If you are concerned about security you need to look into secure communications which are either going to involve VPN connections or HTTPS setups. Depending upon what you are hoping to secure, the Government will still have full access to all of these communications should they choose to take that option.
For banking and other secure activities, you are already secure as long as you ensure that you see the "closed padlock" and/or an HTTPS (the S is critical) in the web address.

Think of email like a postcard. Anyone can read its content along the way.

Do the Lois Lerner lost email approach every once in awhile then set up a new account.. No body can find them!

Used Yahoo for 5 years no problems