Franky, with the slope, I might suggest moving away a bit from a "conventional" floor plan. Since it's quite a steep slope, split-level is probably not the best choice (but you might want to take a look at matte's house here, for me that's a brilliant split-level solution). Nevertheless, you can take advantage of it. Without further specifications, a basic idea that comes to mind is:
Very schematic: two levels, offset against each other. If I understand correctly, the lower level has to be quite deep into the ground (here the terrain profile is shown by the red line) in order to comply with the development plan; possibly it has to be built deeper into the ground on the sides, so only windows to the front. Advantages are that you probably don’t need that much excavation and you get an amazing terrace on top and still get sunshine below (with a balcony it tends to be dark underneath). From the street side you only see one level. The whole thing can appear modern with a flat or shed roof (does the development plan allow that?), or, as I understand, you prefer conventional, with a gable or hip roof on top. If done cleverly, you can go directly from the large terrace into the garden if the lower cube goes a bit deeper into the ground.
Just a thought, without suggestions on how to arrange the rooms etc. But in my opinion that way the plot would be optimally used without forcing a house planned for a flat plot onto one with a strong slope, which only ends in poor compromises.