There is no reason to allow your firewall to use a setting for 'Public' unless you are absolutely certain you will be using wi-fi or cabled connections on public Internet access areas such as cafe's, libraries and/or city/town free wi-fi.
As I suspect, if your setup is permanently based at home, you should ONLY check the box for 'Private'. Domain is for network based client PC's connected to a server and Private is for home or small office use where a server is not used. It is absolutely safe enough to use where setting 'Public' can be risky to your computer and also give away some info through that connection if the details are intercepted by anyone.
User Access Control popups...
When these popup they are there for a very good reason but some people just find them absolutely annoying.
If you want to turn them off, and as a techie of long standing, it is possible but I wouldn't recommend it. However, here is how you do it...
Once the popup shows click the text link that says "Show more details".
Next click "Change when these notifications appear".
Then drop the slider to the bottom of the scale to never show notifications of this type. Accept the changes and you may be asked to restart before the changes come into effect.
You may not however, turn ALL notifictaions off via this slider and some may still show. These ones cannot be turned off at all so you will just have to put up with them.
If you find the changes don't stop RM's warning's then only a registry hack will allow the change and I am not placing that procedure on this forum for obvious reasons.
Hope this helps....