You mentioned Java - are you referring to the web JavaScript API, or the Java SDK? I'm guessing you're referring to the JavaScript API (JSAPI) since you are wanting to publish your data to the web. For your reference, here is the link to the documentation:
ArcGIS API for JavaScript
You might want to look more at the WebApp Builder - it's easier to develop web apps than the full-blown JSAPI:
Welcome—Web AppBuilder for ArcGIS (Developer Edition) | ArcGIS for Developers
As far as ArcGIS Server, if you purchased for local deployment, it may be a bit challenging to set-up if you do not have experience with IT/systems, ArcGIS, and web development. There are quite a few pieces to the puzzle, everything from installation, infrastructure and network architecture, to setting-up failovers and high availability, and to making the server publicly accessible. It's doable, most definitely, but many users opt to go the ArcGIS Sever on-the-cloud route, or maybe ArcGIS Online, depending on needs - Deployment | ArcGIS for Server. It's important to understand the differences:
https://community.esri.com/thread/51315#post198140
What are differences between ArcGIS Online, ArcGIS for Server and ArcGIS Publisher? - Geographic Inf...
Here's the installation guide for local deployment:
Welcome to the ArcGIS for Server (Windows) installation guide—Installation Guides (10.3 and 10.3.1) ...
I will say you get the most control by self-hosting ArcGIS Server and developing using the JSAPI API, but it's a process and is the most complicated route. You can even host the JSAPI, if you want. I would say most don't and simply use the Esri CDN.
It took us 6 months+ to install, configure, develop, test, and deploy the first version of our mapping application.
