The most cost-effective solution is a gable roof with a pitch of about 22°. This is the simplest roof shape; a flat roof is, to put it bluntly, only cheaper under the condition that you don’t care about watertightness.
Below the mentioned roof pitch, special roof tiles / stones are usually required, and the entire roofing is more labor-intensive because wind and weather do not become any gentler, and roofs are in a way "dry stone walls" – with flatter pitches it is more difficult to ensure watertightness, and the roof tiles / stones lie with different pressure on the battens.
With a steeper roof pitch, the roof surface becomes larger, which only makes sense if you use the space underneath. However, it may be that the development plan requires, for example, 30°, even if you have no plans for the attic space.
Giving the roof more inclined surfaces (hip / tent roof instead of gable) means creating ridges where the inclined surfaces meet. This requires angled cuts of the roof tiles / stones on the roofing level, special tiles / stones as with the ridge, and additionally more complex metalwork / tinsmith work. This roof shape is also more complex on the level of the roof structure.
Open eaves themselves shift the insulation into the slope. With hip or tent roofs, it is also difficult to aesthetically coordinate the ridges with the course of the interior walls. The sloping "ceiling" then practically has dog-ears. If you hope to save money with open eaves: that is clearly a top-notch backfiring move.
Besides roof shape and pitch, there is also the dimension of the roof construction: trusses are cheaper than rafters, and there are again different types (studio trusses and the practically very "in the way" timber-frame trusses in the attic).
By the way, there are also solid roofs, and this list is by no means complete. That’s just a preliminary explanation to outline the price-influencing parameters for you in basic terms.