I am in the middle of developing my first C# ASP.NET (v 4.5.2) Web API, and until now i have been only using Visual Studio 2015 Professional, with IIS Express 10 for debugging.
I have no previous experience with IIS or ASP.NET deployment in general.
So my questions :
if you take a new version of IIS you should not have to install .net frameworks. If the target framework does not exist on that server, you have to install it and register for iis : https://msdn.microsoft.com/de-de/library/k6h9cz8h(v=vs.100).aspx
The nuget packages won't be a problem because Vs will deploy all dlls too (like on express)
If you are using some special things like Url-Rewrite you have to install these modules manually (e.g. for url-rewrite https://www.iis.net/downloads/microsoft/url-rewrite)
About the version, if you want to do it easy, just use the newest. But it depends on which server-version do you use, even though most applications work on older IIS too. Maybe some changes in the web.config have to be made if you are using some kind of "special" configurations
For deployment you have several options:
Deployment over FTP/Fileshare - create on IIS an Application - ensure that the right .net framework is selected - create fileshare or ftp - then deploy it into the directory, which is app-directory