What do you want out of upgrading cassette? If during your normal riding, you are not needing a lower gear to get up a hill, or a higher gear for when you going fast, then there is not much point to upgrading the cassette.

On a modern bike with indexed shifters, you almost certainly need to keep the same number of gears on the rear unless you are going to change the shift levers too.

Also, you need to be sure if that is actually a cassette. If it is instead a freewheel, then a wheel with a freehub on it is not going to work.

A bike shop will probably charge you less to fix the spoke than you can buy a new wheel. But simply buying a cheap used bike with the correct number of gears on the rear might get you a replacement wheel for just a few bucks.