The main thing you shouldn't do is throw batteries, light bulbs, and other hazardous waste into regular garbage bins. They contain mercury, lead, and other chemicals that pollute the environment, so you need to dispose of them separately. Usually cities have special hazardous waste collection points at electronics stores, pharmacies, or car service stations. Before you start sorting, find information about such places in your area - online or ask your building management company.
About bottles and regular plastic: you do need to rinse them, but don't go overboard. Just a quick rinse to get rid of food or juice residue is enough - not only for the convenience of collectors, but also because dirty plastic doesn't recycle as well. Glass, metal, and paper should also be cleaned before disposal if possible. Containers usually work like this: plastic and metal go in one, glass in another, paper and cardboard in a third, and organic waste in a fourth (if available). But there can be regional differences, so check the containers themselves - they usually say what goes where.
If you're unsure where to put something specific, the logic is simple: plastic tubes from creams, plastic bags, and other similar stuff goes in plastic - same deal with polyethylene. And caps and parts made from different materials don't need to be taken apart, just toss them in with the item. The main rule is: if it's not a battery, not a light bulb, and not hazardous waste, it'll get recycled somehow anyway, even if you mess up the container a bit.