You'd need to look at the specifications of the individual appliances. Induction cooktops are typically power hogs in their won right.

60A requiers #6.

This is probably not the answer you want, but call an electrician. You are asking about a fair bit of work, which may require a service upgrade. You should have a load calculation done to determine how much demand is on your existing service- if you add a subpanel, you could trip the main due to overloading. BTW, 60A may be too small for the load you want to connect. Evaluate the existing service first to avoid potential problems, then load calc for your new work. Get several estimates- best value may not equal cheapest. Good luck!

Mike

As you are remodeling, you should bring your kitchen up to current code.
Including:
Two 20 amp, GFCI protected, small appliance circuits.
Separate circuits for appliances such as refrigerator, dishwasher, microwave, etc.
I would also put all kitchen circuits in the subpanel rather than leave some 40 feet away in the main.

That is a mischaracterization of the requirements.
The code requires two (at least) two small appliance circuits serving all the receptacles in the kitchen and NO OTHER OUTLETS. Only the countertop receptacles are required to be GFCI protected. There is no code mandate for separate circuits for individual appliances unless their installation instruction requires it (though it's not a bad idea).