[Noob] Backing up phone info before hard resetting

Hi,
I am a huge Android Forums newbie, but I really needed help with backing up my phone information before hard resetting.
Basically, the primary email that the phone is running under is an email for a company I no longer work for so I don't have a valid email there. Because I can't log into my work email, I can't log in and download any new application so unless you guys know of a different solution, I guess my only option is to hard reset and then make a new primary account.
However, I would like to save all my contacts and texts messages [if possible, although I hear it's unlikely], but since I can't download any new applications, I also can't download any storage applications for my phone.

So how do I proceed?
Thanks in advance!

 

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