First problem I see here is that the OP is posting from Serbia. I don't know how available or expensive a lot of this stuff is there. I think Eastern European countries don't have the throw-away culture we have here in North America, so all the soft drink bottles may be glass (deposit for the bottle, for all I know.) Paper towels (throw-away thinking) may not be common there.
Saran wrap is a brand name, not generic and OP may not recognize it. (kind'a off-topic, but "saran" in Serbian (Шаран in Cyrillic) means carp--and I think they wrap their fish in newspaper.
Some steel cans, not all, have plastic on the inside of the can. All steel food cans are galvanized steel: They have a thin coating of zinc on the outside at least, sometimes on both sides. It's the zinc coat that gives the vigorous reaction between cans and copper. The steel-copper reaction is much calmer. The steel-zinc reaction is pretty active too--if you cut or scrub galvanized steel, a lot of the electron exchange is going to be between the steel and its zinc coating and less current between can and copper.
And I have no idea whether they market plastic-coated (on the inside) steel cans in Serbia, anyway. Galvanized steel cans have been used far and wide, so the zinc-steel-copper three-way will be a serious consideration in designing the battery. If it can be constructed without cutting through the zinc coating, it can make a good battery until the thin coat exposes steel, which won't take long, and then we're back to the 3-way reaction.
I also have no idea if Home Depot has any outlets in Serbia, nor how available (and expensive) strips of pure copper are: Serbia has lots of copper but its industry declined drastically in the 90's and it may not refine its own copper. Only pure copper is effective as a battery electrode because impurities will cause local reactions in the metal surface, draining electrons away from the cell flow, just like the zinc and steel once the coating is breached.
Here in North America, we have piles of food cans and scrap copper all over--electric wire, for example, is pure, electrolytically refined copper, and it's not hard to find scrap wire. I suspect in Serbia, "scrap" metal of any type is harder--more expensive--to come by.