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I've been pondering the same question and have not come up with a definitive answer yet.
The best solution acc. to my research would be glass. It's completely inert and very stable. You just have to make sure to keep the light out. On eBay I found 10l and 16l pickling jars that would be suitable. They are of course much more expensive than a comparable plastic container, but will make up for it with longevity.
Porcelain is also a great material, but even more expensive than glass.
I would be suprised if there is an actual relevant amount of chemicals leaking from Hydroponic containers.
Hmm. I would assume plastic is a better material than metal. Hydroponics solutions can be a bit acidic which will dissolve metals. Plastic is mostly inert as long as sunlight doesn't eat away at it.
One possible solution would be to wrap your plastic containers in something that blocks light (or, more accurately, UV rays). Off the top of my head, I’d suggest coconut mats or something similar. They also look a bit nicer than sauce buckets.
I would worry more about if the containers allow any light through to your water - that can cause your water to get gross real quick.
Can you get some clay?
Lining the inside of these plastic buckets with impermeable clay should provide a barrier that prevents any bad plastic chemicals from getting through to the plant inside. Being supported by plastic means the clay can be thinner and doesn't need to be fired to be stable, so it's cheaper and easier than making your own clay pots.
(Though if you have a good natural source of clay nearby that you won't get in trouble for taking from, making your own earthenware pots from scratch could be very rewarding. Look for the "Primitive Technology" channel on youtube for some examples of how simple that can actually be to do.)
I've thought about this. It's likely going to be very messy and clay will never be waterproof unless you fire it or use some chemicals which are worse than the plastic.
Clay is porous even when fired
They’re initially food safe material and all you have to do is wash out the sauce residue. The problem is though that this food safety won’t last long in sunlight.
I mean those seem like a good resource, but you are also talking about a small balcony garden. It might be fine. But you are probably only going to be building a small system regardless. And at the end of the day, the buckets or whatever else you are growing in, its only going to a small part of a larger overall budget. It might be worth looking into a kit and getting a system that "just works" so you can have a higher chance of success starting out?
You might look at some of these systems for inspiration. Granted they are aquaponics but its not going to be that different in a pure hydroponics set up.
https://www.waiaholenursery.com/backyard-aquaponic-systems.html
I think one of these could easily fit onto one side of a balcony.
I’m trying to avoid plastic whenever possible
I mean you are intending to grow in a pretty contrived, artificial, engineered system. Its just.. It seems like mixed motivations here. Like, either you want to grow in a more organic, less constructed system (like in ground beds or furrows) or you can't? Like, there are other ways for to grow food that just start out at a much less baseline level of plastics (just having some plants in terracotta pots for example). And like, if you no like plastics, thats fine, but like, maybe hydroponics isn't something you want to do then. Its basically gardening with plastic. Which I don't think is a problem. I couldn't garden without plastics, or at least, I'd have to put in thousands more hours into weeding or I'd have to spray. Most commercial growers have to make the same choice, between plastics and spraying.