A few new stainless steel pans

Hello all,

I’m looking for some buying advice on a few pots and pans. I will be moving from the UK to Israel in late summer and would like to buy before I go. There is an awful lot of information on here and elsewhere and I’ve been a bit overwhelmed by it. Any help is most welcome.

What I’m after:
Saucepans – Matching set
14/16/18/20cm – Lid is optional for the 14cm
Sauté pan - Doesn’t have to match the saucepans.
24cm – With lid.

Budget is roughly £300 - €340 - $415. But I might flex for a great deal on something better.

Items must be available to ship to the UK.

I’m looking for stainless steel. But don’t mind if it’s 3/5/7/ ∞ - Ply. Or with just a heat diffusing plate at the base. Just the best for my budget.

It needs to be dishwasher friendly. Whilst I don’t mind doing one or two pans by hand. I’m not doing all of them that way.

Very happy to wait for sales or set up price alerts on the European amazon sites. But advice as to what actually gets discounted and when is appreciated.

If there’s a set that includes the above at a good price, I’d be happy to go for it. But most seem to include things I don’t need.

Right now, I cook on gas. But I’ve no idea what I’ll be using in future, so it needs to be induction friendly.

I’m mostly cooking for just 2 people.

What I currently have, roughly sorted by how frequently I use them:
Sauté pan - Darto 25cm – A new favourite, though a lid would be nice.
Sauté pan – Greenpan 28cm – Kind of surpassed by the Darto, still used for acidic things. But has always been too big.
Saucepans 14/16/18/20cm - Cheap Ikea or similar, very uneven heating so anything that might stick currently goes in a sauté pan.
Casserole – Staub ECI 24cm – Great for slow cooking, also used for baking bread.
Frying pan - Greenpan 20cm – Mostly used for eggs.
Frying pan – Tefal non-stick 28cm – Not used often.
Griddle pan – Cheap cast iron – Not used often.
Stockpot - Ikea 365 24cm/5L – Rarely used.

Thanks in advance,
Tom