For most applications that don't involve heat, pretty much any glass container will do in place of a beaker or flask for a lot of experiments. Clean jam/pickle jars and glass bottles make for decent, free beakers and chemical storage. If heat is involved, PYREX glassware is a good idea. That said-- Home Science Tools has really affordable glassware, of good quality in my personal experience.
While drugstore-quality chemicals are a no-go for most "real science", they will often do just fine for demos, where precision and accuracy are relative non-issues! For instance, there's no reason you can't use Milk of Magnesia as your magnesium hydroxide (Mg(OH)2), or plain tap water in most demos.
Lab spaces use purpose-built lab supplies like weigh boats, microspatulas, pipettes, and funnels. These make good sense for sterility and other factors in a lab setting, but for demos, you can often make do with squares of foil, cutlery, eyedroppers, etc. Be creative, with a mind for safety!
While many demos can simply be disposed of down the drain of your sink, others require a 'properly labeled waste container'. Most universities and institutions will have a division dedicated to lab safety and waste disposal, and will have their own procedures for proper chemical waste. If you are demonstrating at one of these institutions, you are in luck! You should communicate with the relevant division about how best to do this.
If you are demonstrating at home or are otherwise without a dedicated waste disposal service, most cities have at least one public or private hazardous waste disposal service, who will take your waste, usually for a nominal fee. Make sure to follow the directions provided by your local waste disposal authority for handling and packaging your waste!