A ventilation system isn't strictly necessary with a heat pump, but it makes a lot of sense under certain conditions. The key thing: heat pumps need a relatively airtight house to work efficiently. If you're sealing your house up properly during renovation anyway (new windows, better insulation), you run into the problem that natural ventilation through cracks and gaps disappears. That's where controlled ventilation comes in - it makes sure moisture and CO2 get out and fresh air gets in without you having to constantly throw windows open. It also saves heating energy because you're not wasting heat by heating with open windows.
The combination is especially worthwhile if the ventilation system has heat recovery built in. The warm exhaust air transfers its heat to the fresh outside air before it leaves - that significantly cuts down your heating needs. Without ventilation, that would be a huge waste with airtight renovation. But you can also just install the heat pump first and retrofit a system later if it turns out you need it.
On the costs: a decent ventilation system with heat recovery will run you somewhere between 3000 and 8000 euros depending on size and quality, installation included. Heat pumps are similarly expensive, but it depends a lot on the type (air, ground, water). All told you should budget 15000 to 25000 euros before you factor in subsidies - and there's quite a bit of government funding available right now that can cover a large chunk. But it pays for itself in the long run through savings on heating costs.