The best way to do videos is always to host them on AmazonS3 and serve them from there. Personally I use flowplayer because it is easy to set up. The free version can be downloaded from
https://flowplayer.org/pricing/#downloads.
You just put all the files in your S3 bucket and edit the player page. Here is an example
http://freevault2.s3.amazonaws.com/immasterclass0514/test.html. If you look at the page source you can see how simple it is. That example is using flash which is the simplest but nowadays you should be looking at html5 and provide your videos in both mp4 and webm so they can be viewed on mobile devices as well. I am in the process of redoing my videos to provide that bit it's a wee bit more complicated.
Where you have the access is immaterial. You can also get a WP plugin from flowplayer which makes the process of using HTML5 a lot easier if you intend to add videos to your blog. I recently tested it to see how it worked for laptop and smartphone and it altered the size to suit the screen automatically.
If you need any help pm me.
PS Never try and host videos on shared hosting. Even a short sales video will get your site pulled no matter how often the customer services team tell you it will be OK!!