You do know there is no relation what so ever between gaming lag en setting the graphics level of your game right? It's not like the game is sending a screen capture to the other players.
So you have 2 issues. The first is the graphical performance of the game which is depending on your machines power. Which you should ask in a different subforum.
The second is the networking speed which might cause lag. You don't need a uberspeed internet connection from your isp. 10mbit would be more than sufficient probably. Depends on the game. Getting wireless would be simply put "a bad idea". Like Iceyn1pples said the quality or response from your connection is way more important. Wireless connections tend to have lots of overhead. Loads of packets just get lost between your network card and wireless router/accesspoint. Which increases the ping/lag/latency/whatever enormously.
To make a long story short, no matter how fast your wireless is it's always going to be much worse then wired.