over the time as the media content increases you might be paying more if you go with online sites.
Here are couple of option for extra storage for one time cost or free
High quality Unlimited free storage from google photos unless you select the option to store in original size( Most phone cameras are less than 16 megapixels)
Network storage Access storage that can be setup in your home network and can be accessed the content over the web
there are NAS drives available from western digital or buffallo or seagate or synology (from any retailers) which cost around $150 for 2TB space.
these companies have very good apps for mobile or desktop to access the contents over http that you have on your home.
but if you want to access the content over https then you need to setup SSL certificate which cost minimum $70 a year (free ssl might be available end of the year).
I think if you want to store photos and videos and wants access it over the net , it should be fine.
storage expanded as needed as external hard drive.
Another option is to Run/use pogoplug (https://pogoplug.com/) or ditto or similar devices/programs which will either run independently as a device in your home network or run on the desktop
and allow you to access the content through their secure website.
these application license/device cost around $50
to store photos and videos you can use mobiles through itunes.
For important data password protected apps are available for android or iphone which can store data in an organized way.
or carry an portable drive from western digital which comes with password built in or if you use a regular jump drive ,
encrypt it using truecrypt (truecrypt.org) or equivalent software to encrypt the drive.
4tb portable drive will cost around $60.