|Is the device you received from your ISP a "combination" device. Which is to say, is it a modem, a router, and a wireless access point all in one device?|
If it is, you can ask your ISP to provide you with only a modem and you'll provide your own router, in which case yes, you would need to buy a router.
If they won't, then there's nothing anybody can do for you except to do what's already been done.
Just FYI, it's not harmful to your laptop to leave it up and running all the time so I'm not sure what your aversion is to doing so. I have about 6 PC's in my home office and some of them are 10 years old and have been running 24/7 the entire time I've owned them. It's harder on the moving parts (most specifically the hard drive) to shut computers off and turn them on all the time than it is to just leave them running.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.