Any systems that do the encryption for you or rely on the browser doing the encryption for you are not secure.
If you rely on an OS by Microsoft or Apple, then you are not secure either (there are backdoors in place that will subvert any encryption before/after encryption/decryption, but I guess you'd have to be a high profile target - as far as I know this is not routinely done, it would be too obvious); not saying an open source system is foolproof, but you're lightyears ahead using Qubes or OpenBSD instead of Windows.
Unless you know what you're doing, secure communications on a mobile device is much harder to achieve. And like the recent Stagefright Android security advisory demonstrates, these devices are especially vulnerable. Also in no small reason because in all but a few,
the baseband processor essentially has free reign over your mobile device, rendering any app or os-level protections essentially useless;
This does a fairly good job of explaining this problem and some others, and it is, in my opinion, an interesting read.
Unfortunately, even on desktops or laptops the security put in place by the OS can be potentially bypassed in
certain other ways (of which the linked one is but one among many).. your network card essentially has free reign over your whole computer memory, and any exploitable bug in the cards' firmware means game over. The network card is connected to a global computer network. You see the problem.
The strength of your email encryption will only be as strong as the security of your whole system [weakest link]. For instance, if you have a keylogger installed, encryption is essentially useless. You need to secure your system to the best of your skill if you're going to do anything important with your encrypted communications; If your key passphrase is 'lol123', it won't be very hard to crack.
Regarding the security of email itself, it's simple: what you want is end-to-end encryption, like GnuPG. Use >=2048bit keys and make sure to confirm the fingerprints through another secure channel.
Also, if you can use Tor and a service which supports emailing to .onion addresses (like sigaint), then that is ideal, as there will be less metadata being generated - your email will never leave the Tor network then.
As a further step, you want to create different identities for different contact groups, and use something like
The Tor Browser so that a) your browser fingerprint is the same as millions of others, and b) your location is concealed; the idea here is using the providers' webmail rather than directly sending over SMTP (even over Tor); less information to fingerprint and uniquely identify you this way.
To sum it up, ideally use an open-source operating system, prefer desktops/laptops to mobile, don't install any more software than you need to, prefer open source software to commercial software, use GPG (GnuPG), prefer emailing over ther Tor network and using webmail rather than smtp/smtps, and make your key passphrase strong.
Additionally, encrypting your entire hard disk is almost never a bad idea. Just remember that it is easy to recover the encryption keys and thus bypass the protection that disk encryption offers if your laptop is seized while it's suspended or hibernating (there are some possibly mitigations if you *hibernate*, but lets not go there here). I would recommend shutting down the laptop for instance while crossing borders.
This is the time to really find out who you are and enjoy every moment you have. Take advantage of it.