Limescale and strange taste are two different things, and that's the point others haven't really emphasized. An under-sink water filter helps you with sediment and limescale, but if the taste comes from residual chlorine or other substances dissolved in the water, then yes it works. The problem is you don't know which of the two factors is your real issue until you get it tested. Contact your water utility (it doesn't cost anything) and ask for the water quality report: there you'll see exactly what's in it, and from there you can figure out if a filter is really necessary or if you can solve it with simpler things.
If you find out that limescale is the real problem, then yes, a water filter with odor filter + one with activated charcoal works. On Amazon you'll find decent brands (not just Aqua Optima), but the maintenance cost is serious: filters cost 20-40 euros each and you really need to replace them every 6-12 months depending on how much water you use. If there are two of you at home and you drink little tap water, maybe it's not worth it; if you drink a lot, then you start saving compared to bottled water.
What I'd suggest is don't fall into the trap of someone selling you a water filter without first knowing what it actually filters. Some reverse osmosis systems are excellent but cost more and use water; simple under-sink ones are cheap to buy but require discipline with filter changes. Do the test first, everything else comes after.