What material should I choose to replace old water pipes?

We had a similar situation at home - copper pipes started leaking after about twenty years too. In the end, I went with reinforced polypropylene, and so far no issues. Its main advantage is that it's about three times cheaper than copper pipe, it's easier to install (I handled half the work myself), and it lasts at least forty to fifty years. The downside is you need to protect it from sunlight if the pipes are outside or in a room with windows, otherwise it degrades faster. You also have to be careful with hot water - you need to monitor the temperature.

Metallic composite is a compromise between convenience and reliability. It bends by hand, which is really handy during installation, doesn't require as many fittings as polypropylene, and looks neater in your interior. Usually lasts twenty to thirty years, but there's a catch - over time, oxygen can seep through the polyethylene layer into the water, which causes corrosion of the system's internal parts. Not critical, but annoying.

New copper is beautiful and reliable for a very long time, but the price is just brutal for a complete replacement. Only makes sense if you've got the money and want to do it once and be done with it for good. If your budget is tight, I'd recommend polypropylene - the most practical solution for a private house. If you want something in between polypropylene and price, then go with metallic composite.