Both Weather Display and Virtual Weather Station have their pros and cons. Both programs are stable and still being actively developed. Weather Display has a lot more features, uses less CPU resources, and offers stronger support. VWS has a more intuitive user interface, produces prettier graphics output, and has a good website builder for your first weather Web site.
I actually run both at the same time, thanks to
VirtualVP, which allows you to run up to 4 weather programs at once. You could do the same thing... continue to run VWS while you try Weather Display.
Both VWS and WD will upload to web sites. WD also supports webcams, although for that I use
ImageSalsa, one of the many webcam software options available.