Welcome to SP!
While I do not have experience with Azure, my question to you is: Do you think you are developing anything sophisticated enough to warrant hassling with a cloud setup?
Clouds are really targeted to those with large scale sites that anticipate seeing significant growth in the future. There is a long gap between the points where you'd start to reap the benefits of a cloud service. There's plenty of hosting plans out there (much cheaper by the way) that can handle probably 90% of web sites that are built, before any "scaling" is needed. Sure deployment might be made easier with Azure, but ask yourself if deploying your app by yourself is really that difficult.