Did you mean this board?
Yes. There are other types of Ethernet shields, but the ones based on the Wiznet chips are much easier to use.
Don't you suggest should I go for a breadboard or anything better (pre designed with sockets) since I will be installing more than 1 gas sensor?
Yes, a breadboard is useful, along with wires, a soldering iron, solder, heat shrink tubing, a multi-meter, and a host of other things.
Is it possible to send data on a website using GPRS module?
It is. But, GPRS modules and associated hardware, and the ongoing cost of a SIM card, are much higher priced, and difficult to use, compared to an Ethernet shield. I'd start with the Ethernet shield. If you need to go wireless, a WiFi shield would be my next choice, if there is WiFi in the area. Only if WiFi and wires are not possible would I go for the GPRS module.