Securing your smart phone.
First, if security is really important while accessing the Internet via smart phone, toss your iPhone in the trash. iOS is closed programming by Apple which is known to cooperate with spy agencies. Get an Android phone or tablet.
Use a password so your phone is locked in case you lose it.
Yes, Android is Google and they, too, cooperate with people who want to spy on everyone. The difference is that Android OS is open source and the code can be seen and studied by anyone with the knowledge to do so. You can also unlock and gain root access to your phone's os ( may void your warrantee ) where you will find out it is basically a simpler version of the Linux operating system.
Since you can install apps designed with security in mind including a version of TOR, encrypted email clients, VPN and much more, you can wrap a cloak of anonymity and security around most text or browser communications that enter or leave your phone.
If you transport or otherwise keep secure data on your phone, encrypt it. There are programs that are compatible with TrueCrypt which means you can encrypt and then transfer those files to your MicroSD card where you can decrypt them on the phone if you need to.
HERE is a page with information on using Firefox browser with a plug in to proxy your connections.
Guess what...you can actually install and run Linux on your Android phone !
Blackberry has a reputation of providing the best security for text communications out of the box but I doubt it has as many add on applications to cover as many scenerios as does Android. President Obama uses a Blackberry which the CIA custom modified for stronger security. You cannot get one of those !
Here is one article about smart phone security. CLICK
Note there is a conflict in that it is often considered that you undermine your security when you "root" you phone, it is also true that some security measures cannot function unless you phone is rooted. You need to study the pros and cons of your needs and situation. Sometimes it is only necessary to root the phone to install the program, afterwards you can "unroot" the device for daily use. Not all situations are created equal.