This:
"I am happy to drink tap water but for my own health I would like to find a small water bottle that filters the water for chemicals or
minerals, not diseases which I know are not in water supply."
Caught my eye. When you refer to "minerals" in water, you're referring to ionized inorganic constituents dissolved in the water. These are not removed by filtration -- they pass right through because filters are designed to remove suspended solids (particulates) not dissolved ions. If the filter contains activated organic carbon it can remove some organic contaminants and a few inorganic contaminants, but most dissolved constituents pass through.
My advice for you, if you choose not to drink tap water, would be to look at the label on the bottled water you're considering and choose one that has the lowest level of "TDS" or total dissolved solids. Use google translate or bing translator to figure out how that is worded in whatever language used where you are. Anything below about 500 ppm, or milligrams per liter, probably won't cause you problems. Anything above 1,000 ppm, if you're not used to it, may cause some people problems, especially if it's high in sulfate, which can have a laxative effect for some people when present at high concentrations.
But don't kid yourself that bottled water is necessarily better for you than tap water. I was in Italy a few months ago and went to the trouble to look at the nitrate concentration in the various bottled water products I came across. If I recall correctly, only one that I encountered was below the U.S. EPA's maximum contaminant level for nitrate of 10 ppm. Values of 12 ppm or 14 ppm were common. Granted, EPA's value is for long-term exposure and is aimed at preventing methemoglobinemia (blue baby syndrome) in infants. For short-term exposure, the World Health Organization's recommended value is 50 ppm of nitrate.