You may or may not have luck with secondhand pots and pans. If it were me, for the right price, it wouldn’t matter if they got abused.

My frying pans from Made In are great, but they have no helper handles. They heat very evenly and I have had great results. I was able to make eggs in my uncoated pans and I very often did not have problems with sticking. (This was not the case with my old frying pan that bit the dust. Uneven and lots of sticking.)

Cuisinart and Tramontina are both pretty great. I have a stock pot, a 8 quart pot, and sauce pans from these brands. Not super expensive and can handle some abuse. I got the recommendations from Serious Eats and am happy. I would recommend you look at these if you want to buy new. I got these to replace hand-me-downs and secondhand stuff I got that was thin and single ply. Couldn’t afford All-Clad. When I got them, I thought I was going to be counting the days until I could replace them, but after using them, I’m in no hurry. I haven’t measured, but they are thick and haven’t shown any signs of warping.

Whatever you do, do not get anything with nonstick coating. You need to baby it and it still wears out too fast.

Made In makes a universal lid that may interest you. My partner doesn’t have the patience to find the right lid so she uses it a lot.

I agree that helper handles are great for larger capacity cookware but it would seem more cumbersome for smaller items like an 8" frying pan or a smaller saucepan. You can get a 12" frying pan with a helper handle, but smaller will be difficult to find. You could look into saute pans, which are very versatile and usually have helper handles.

Depending on how much money you’re willing to spend, I would go with a relatively inexpensive set/get a few individual pieces from Cuisinart or Tramontina. In my experience, their stuff is awesome for the price. I haven’t regretted my purchases from them.

I had a secondhand pot that had a second bottom stuck on to even out the heating as far as I could tell. It fell off. Maybe fixable.

I had it for 10 years so I was satisfied I got my money’s worth and bought myself a much nicer pot.