Any Arduino will be able to deal with 4 analog signals and run an Ethernet or Wifi shield. You won't get 12 bits of resolution, though, except on the Due.
If you are sending data to Matlab for further processing, it doesn't make sense to use the Arduino to connect to the internet. Use the PC that Matlab is running on to deal with all data coming from the Arduino, sending it to Matlab or to the internet, as appropriate.