You can upload to WeatherLink.com and access your data on your computer or smartphone with WeatherLink mobile app. You do need a Davis data logger to do this, as well as the station.
The best web interface, IMHO, is to install use Davis' WeatherLink software, then install the Weather Underground plugin and upload your data to wunderground.com. Forget the problems of running your own web page server etc. I tried it and its a lot of maintenance. True Davis' software is 1990's vintage. No modern UI. But once you get past installing the RS-232 serial to USB converter software (silicon labs dll - yup that old!!) it all works. I am running it on Windows 8.1. So once you get your station (the vantage vue is great), get yourself a Wunderground account and set up your personal weather station site with them. It is less hassle than developing your won website.
The Davis Vantage Vue is a fantastic choice for a weather station. I have owned one for a few years. I first started with the USB interface to connect to a desktop PC. That worked very well for a while, but with power outages lasting longer than my UPS would handle, I would lose connectivity to wunderground.com until I restarted it. Finally, the hard drive died, not the fault of the weather station or software. I then opted for the direct to network plugin called WeatherLinkIP. This allows you to go direct from the console to your router WITHOUT A PC to stop or fail..... The only maintenance I have done is replace the battery in the weather station after about every two years. The hardest part of the installation is making sure that you actually know where NORTH is to point the station.