I purchased the Personal use of Arcgis desktop. I'm not sure what to download or the order of downloads. I downloaded the first few things and I can't open arcmap or anything (Nor is it even showing up on my computer yet). I can't find a tutorial for downloading/installing GIS anywhere.
Once you purchased the software you should have received an email confirmation with the link to the downloads. Depending where you are located you can try: my.esri.com or accounts.esri.com
Once you have signed in, using your ESRI credentials, there should be various tabs for download and licensing. Mine are under the "My Organizations" tab but I have an enterprise license.
Start with the Desktop 10.x version installation and add the other needed components. The Desktop install covers the majority of the needed components.