Rov is trying to be helpful, but his information in the first answer is totally incorrect.
You do not need HDMI cables running to the Dish, the existing coax cable that is inplace is the correct cable. you also do not have to worry about quad LNBs as you said in your question it's a communal system.
Now there is one issue that you should be aware of, and that is the requirement for any freesat box that has a built in hard drive recorder (i.e. similar to a sky+ box) to have two separate feeds from the dish. so if you have two separate outlets on the wall for the satellite dish then you can get a freesat box with a recorder built in, if you only have one feed from the dish then you can only use a freesat receiver with no built in recorder,