which arduino can you suggest for my project ?

Projects General Guidance
1

Here is my project.

"The students will design and construct a electronic circuit that generates random sequences of binary bits and serves them as integers to the server or to the internet and show them on the LCD."

It have to be 16 bits (from 0 to 32768)

I will use random() OR randomSeed() function.

Which arduino can you suggest to use for this project ?

2

I guess the Uno will do with an ethernet shield (even the enc28j60 if you wan't to go cheap)

set it up with the client library for the appropriate shield (Wiznet or enc)

I think this all is no problem but your still a bit vague

3

What you need to perform actually i mean what you actually mean by this >> or internet, if they are going to generate bits at several other places then let them generate on their separate arduino's and then just communicate with a Master Arduino via. XBee's or Bluetooth or inexpensive RF Radio modules that's it. with your rather incomplete information i think you need this.