What's actually in your water
Choose a cartridge for the problem you have rather than for the longest list on the box. Some of these a filter jug solves completely; some it barely touches, and a couple it cannot address at all — which is worth knowing before you spend money on one.
Start with your own water report
Everything on these pages is general. Your water is not. Hardness, lead risk, nitrate levels and whether the supply is fluoridated all vary by street, and every water supplier in the developed world publishes a quality report for your address — free, and usually within two clicks of their homepage.
Read that first. It converts this from a guessing exercise into a shopping decision, and it will often tell you that the thing you were worried about is not present in your supply at all.
One thing it will not tell you is lead, because lead comes from your own pipes rather than the mains. That one needs a sample from your tap, which most suppliers will test on request.