Do you cook every day or just on weekends? That changes the equation quite a bit.
I switched three years ago and honestly, the savings on your bill are noticeable but not spectacular. We're talking maybe 15-20% less on the cooking part, not cutting it in half. What is true is that it heats up much faster, so in real terms you use less energy. With a normal ceramic cooktop that's 8 years old, the investment in the new cooktop plus the cookware is going to run you somewhere between €400-600 easily. At that savings rate, it's going to be quite a few years before you break even.
As for the cookware, that's where there's the least drama. Like they said above, 90% of regular steel pots work fine. I replaced mine because I wanted a new set anyway, but I could easily have kept using some of the old ones. The only thing that doesn't work is pure aluminum or copper. So if your kitchen is in good shape, you could switch the cooktop without touching the cookware and just replace things as they wear out. That said, note that induction requires you to be more careful: you can't just leave the pot anywhere on the cooktop or it won't heat, you need it centered. It's a small but real change in habits.