"Can't understand the point of paying more for wireless broadband if I can just buy a router which will do the same job so am I missing something?"
Yes, I think you are missing something.
Broadband is broadband is broadband to the point where it enters your house.
It only becomes 'wireless', if that's what you choose to do, within your house.
As you say, you can use a router to wirelessly connect laptops/PCs in a number of rooms throughout the house rather than running wires all over the place.
"not sure whether this would be compatible with the Acer OS?"
The OS is irrelevant. As long as your new laptop is wi-fi enabled (and most laptops are nowadays), that's all you need.