How to store files in website/server cloud

So I want to make a website to store select files from my computer on a web server so I can access those files wherever I go. No, this is not your average Dropbox or Google Drive functionality, it will have more.

So how would I do this? What language do I use and what can help me make this? I want to be able to select a file on my computer, and upload it to the website. The website will store the file and I can visit the website from any computer and download that file. It will be able to do this with multiple files. Thanks in advance.