dedicated server image hosting

I'm building a web-app that is a personal project for some months now. The project revolves a bit around the idea that people can save pictures and share them. Thus I need a high storage space for my pictures. I'm totally clueless when it comes down to webhosting, I never hosted a website etc. At the moment the project is running on localhost and the images are saved on my computer. However I checked a bit some dedicated servers options and I saw the internal storage space was kind of limited (2TB or so). I also see that when uploading an image here on stackoverflow there is a little message " powered by imgur ". So I'm wondering what are my options here ? Should / Can I make an account on imgur and save in there an infinite amount of images ? Or are there other options like ( excuse my ignorance) the cloud or special servers to save images ? Reddit for instance seems to save their file on a personal server, links of images on reddit look like this : (http://ift.tt/1JwUPuw)