Just a quick update....
In the end, I bought an inexpensive sort of half-basket from a shop here in Croatia....costs 15 USD...good thing is that it is cheap, easy to mount and take off (simple hooks) and not a typical lady style basket.

Busy Basket / Naslovna / Busy Basket - Ko?arica za no?enje prijenosnog ra?unala i poslovne torbe na biciklu

So far it feels good, very practical, no worries of anything being stolen, balance is fine, my only worry is that it might not last too long, as it jumps a bit when I meet bumps on the road, and it is not top quality built.
But it is as cheap as possible....

thanks to everyone!