This site, which covers some aspects of Earthship water design, may prove helpful:
Earthship Water System
The climate is obviously different, but some principles will be exactly the same. For potable water you wish to insure that it never comes in contact with anything toxic. This starts with the roof (as in no asphalt shingles), or however water is collected, to pipes, storage containers, etc.
There are many sizes of plastic containers designed for potable water storage. Some containers are not designed for potable water, so know the difference. Vendors of those that are will state so quite clearly. Something less expensive would be to build your own cistern out of something such as concrete. A plastic coating can be easily applied which prevents leaks and makes this ideal for potable water. Make sure the coating is designed for potable water. A good place to look for these are suppliers that deal with fish ponds and such.
I'm more familiar with temperate mountain than tropical settings, but would guess you would have more of an issue with such things as algae growth. The basic principle however is to keep the stored water sealed from such things as mice, etc., and also dark. Keep the water from light, and keep it dark. Also as cool as possible, and for this and several other reasons not a bad idea to bury the cistern. Some will advocate chlorination or other chemical remedies, but these can be entirely dispensed with (and yourself better off) if the entire system properly designed and built. In filtration you have the option of such things as reverse osmosis which will do an excellent job removing bacteria and other impurities, but otherwise not taint the water.
Beyond all treatments you might try, first and foremost insure your water is properly stored. A little research into this will help a lot (there are many fine examples and lots of information available online).