I'm interested mostly in making pure elements, but grabbing an aluminum bottle seems too easy. Also baking soda and vinegar or explosion endothermic reactions are not great for Florida summers. I would suffice for homemade hydrogen. Or good luck halogens. More of a how to than an explanation of the science.
If you want almost pure hydrogen and oxygen just use electrolysis. Please do not do this haphazardly, filling your house with oxygen and hydrogen is an exceedingly bad idea. In general it is very difficult to produce pure or fairly pure elements.