I need all images of my website hosted, so I need a very reliable hosting site which i can pay to sign up . I also need a recommendation for site to host 2 videos which I will put embed on my site. I prefer video upload site with secure sharing (where i can share via password protected downloads)
Can you give us a little more information about the total size of all the images and videos, as this will determine what kind of hosting do you need to begin with. Normally, media-heavy sites are recommended to start at least with a VPS, however if its a relatively small site it can run on Shared Hosting too.
Have a look Amazon's AWS storage service, you pay for GB you use. You might need to code/buy a script to integrate its service to your site though, but it's worth it because of the money you will save in the long term. For just video hosting, check out wistia.com and vimeo.com
You can go with Virtual Private Server where Virtual machines are sold as Service. Amazon S3 is an online file storage offered by Amazon Web Services which is very cheap and reliable. If you want to host a Smaller site then you can opt for Shared Hosting.