For a busy family, I’d probably look at a 28cm ceramic-coated pan that works on induction, rather than going straight to stainless steel or cast iron. Carbon steel is another good option, but it needs seasoning and a bit more care.
The Ninja ZEROSTICK Ceramic Pro looks worth a look at around £65. It’s PTFE-free, induction-compatible, oven-safe and dishwasher-safe, which ticks a lot of your boxes. Just bear in mind that ceramic coatings can lose their non-stick performance over time, even with careful use. [Ninja ZEROSTICK Ceramic Pro](https://www.sharkninja.co.uk/ninja-zerostick-ceramic-pro-28-cm-frying-pan-black-cw30028UK.html)
If longevity matters more than effortless egg flipping, a good uncoated stainless steel pan could last much longer, but it takes some technique to stop food sticking. I’d personally choose the Ninja for someone used to non-stick, especially with a busy household and a £150 budget.