Distilled, de mineralised or de ionised water is the normal choice. I don't think any form of filtering other than reverse osmosis will do any good.

In many areas spring water is fine but I wouldn't necessarily assume that bottled water is ok. Unless you have had previous experience or can get it analysed it may be risky.

In real life, batteries are not as fussy as some think, but certain minerals are definitely bad. Water from de frosting fridges and even rain water collected in plastic bowls is often ok, but rain water in polluted atmospheres or marine areas may not be so good.

Awkward in remote places, but most places have battery suppliers or maintenance people that normally keep something suitable in bulk.

At one time that battery manufacturers would analyse your local water to see if it was safe to use but that sort of service probably vanished long ago.