You need to get an ArcGIS Online for Organizations account. The Getting Started help article touches on this. If you go to arcgis.com, you could sign up for a 30 day free trial for now. Once you have an organizational account, you can Sign In through the File Menu in ArcMap. Then, after you choose to publish a service, you can select My Hosted Services as the connection (your second screenshot). Hope this helps!
What build number are you on? If you are on 10.1 final, you should be seeing your Hosted Services on that page. I remember that at pre-release, you needed to do an extra step- When you click the Sign In button, click Manage Connections in the bottom of the window. You then need to copy and paste the URL to your organizational account from arcgis.com. Save this, then sign in, then you should be able to use "My Hosted Services." This should be automatic at 10.1 final.
I think you need to do the Manage Connections suggestion I had in the previous post. The "My Hosted Services" in ArcCatalog will become enabled once you Sign In successfully using the correct connections. Please go to arcgis.com and log into your organizational account. Then, copy the URL to your organizational account and paste it into the "Manage Connections" section on the Sign In window.
You shouldn't be making a GIS Server connection... The first step is to determine if you have a personal or organizational account. You will want an organizational account to publish services to the cloud.
Once you have ensured that you have an organizational account:
1. Click File > Sign In
2. Put in your username and password and click Manage Connections
3. In a browser, navigate and log into you arcgis.com organizational account
4. Copy the URL to your homepage
5. Paste this into the Manage Connections window
6. Close the remaining windows and Sign In
7. Then, My Hosted Services in ArcCatalog and in the Share As dialogue should appear
If this doesn't take care of it, it might be easiest to log a support request (888-377-4575).
Thanks!
Great directions but what do you do if You have ArcMap 10 version. When you sign in there is no "manage connections" option. thanks