Homemade Cheap Rechargeable Batteries?

I would like to try to make rechargeable batteries, however i don't want to spend like $1000 on lithium metal. It only needs to work and prove that it can be recharged (holds maybe 4 Wh), im guessing if i could get some lead plates and some sulphuric acid i could make some cheap lead acid batteries. I also have quite a bit of iron, nickel and zinc on hand already so maybe something like a nickel zinc battery could be made or nickel iron. Ideally i would rather have a better cost per watt hour than watt hours per kilogram and a better watt hours per litre than watt hours per kilogram. That would immediately make lead acid the best choice but it would also be nice to be able to charge it fast like a nickel zinc battery. It must be rechargeable i don't want to make any of those zinc copper, Baghdad, air, earth, water, over-unity bs batteries.