Welcome to the forum by the way. I hope you enjoy it here and stick around.
ADSL uses a different technology to cable Internet so you would need a Cable router.
If you are not looking for any wireless features and can do with wired cabling around the house, you can get a Linksys BESFR41 router for £30 delivered and this will allow you to share your internet connection.
The router has 4 ports and can be linked to more routers if you ever need to expand your network.
PC's go into the router, and then your cable modem goes into the routers Internet/WAN port.
You can check that router out
HERE
For a wireless solution, you may want to try this one out
HERE