Build a website with map and gis information

I would like to build a website that will have a page with a map.
In that map I would like to dynamic add points with coordinates and lines between them.
I am a .NET developer and I am familiar with Javacript.
What is the right way to go?

With a little search I found arcGIS API for Javascript but it seems that it is not free.
Any ideas and suggestions on better or more appropriate solutions?