Well,
the whole thing about crop factor is lenses! With prime lenses no problem really.
But if you want to use a really fast wide-angle zoom, with a good zoom range, you pay a fortune.
Even when using my Nikon D800 (with uncompressed 4:2:2 HDMI-out) having a 135mm sensor, I can only use Nikon wide-zoom lenses with constant aperture having only a short zoom range, but at least there are good AF-S lenses with an aperture ring that can be declicked.
So with a Blackmagic 4K and a low budget for lenses, you have to live with zoom lenses that have a short range, are not very fast, are not ideal for follow focus and most of all, you have to adjust aperture manually over a touch screen, which is hopeless in many situations.
One suggestion: Use Nikon lenses with an Novoflex EOS EF/Nikon NT adaptor, which allows you to at least have manual aperture control via aperture ring .
Cheers