Hello Daniel,
I just recently went through the topic, but I had very good experiences with your idea of having it planned and installing it yourself. When the topic of building a house became more concrete, I visited several fairs and found a company that could offer me exactly that. They planned the system for me, delivered it, and in the end also commissioned it properly, so it was accurately measured in. That cost me around €7,000 in total. (Wohnfläche 130 m²; 5 x supply air, 4 x exhaust air; without basement) Accordingly, I would say that the €14,000 is very high, even if you add around €2,000 - 2,500 for installation.
Best regards
Christian