Putting a basement under an existing house that doesn't have one is MIND BLOWINGLY expensive. Also, $60K is a lot for a slab repair. Unless the slab is just completely shattered into small pieces, mud jacking companies can usually pick up the whole house and level out the slab without coming near that kind of dollar amount, although I of course don't know the particulars of your house.

If I were you I'd get some other opinions on the slab, and if you can get it done cheaper then save your $$ and put a basement under the addition. A lot more bang for your buck.

"...would it be worth it to just spend the money to add a basement instead of fixing the slab then adding an addition?..."

Do you know what will have to be done to put a basement under a slab on grade house? Hint: Start with jacking up your entire house sufficient to remove a slab and dig a proper basement, including waterproofing and perimeter drainage.