Wireless internet through ethernet

Hello, I'm currently at university and my room is supplied with an ethernet port on the wall to access the internet. I often have a few friends over and we like to play LAN games with each other using my computer as a server. So far we've been doing this by using a Tenda switch but it's really rubbish and takes us hours to actually get us all with a direct connection the my server.
So we've been thinking and thought that we could just get a wireless router and share internet from that, as its new it shouldn't have much problems getting us connected and gets rid of all the cables everywhere. So just wondering if I was to buy a wireless router and connect one of its ethernet ports to the wall, the server to another of the ethernet ports and the 3-4 laptops of theirs connected wirelessly, would it give us an internet connection and a direct connection to each other?

Thanks, Mal.

I suspect you have a combo DSL modem+router, and are attempting to connect the router to that, and that’s causing the problem. If so, you need to place the DSL modem+router in “bridge” mode. Then it will work.

[dsl modem+router (bridge mode)]<-- wire -->[airlink router]<-- wire -->[computer]