You need to define what YOU mean by portrait.
Portraits runs from multiple person group (family or wedding party), to couple, to single full length, to waist up, to head and shoulder, to head, to tight face.
The tighter the shot, the longer the lens you need.
IMHO, a "normal" lens is rather too wide for head shots. And as was said, you do NOT want to get too close, or you start to get facial distortion that is usually not pleasing to the subject, and you tend to intimidate the subject with the camera practically in their face. If you want head shots, then you NEED a longer lens.
The common 6x6 portrait lens for the Hassleblad is the 150, with some preferring the slightly longer 180 or even 250. The difference is working distance and resulting perspective. Example, I might use the 150 for head and shoulder, the 180 for head, and the 250 for face. But if I had more working distance, I might use the longer 180 for head and shoulder.
So, if you want to do a lot of head and shoulder portraits, I would get an interchangeable lens SLR. Then you can more easily select the lens you want.
You need to define what you mean by "budget medium format camera." Specifically, define "budget."
Because you can indeed get a Hasselblad 500/cm for what I call a budget price. I got a Hasselblad 500/cm + back + 80CF lens for a fair amount less that I paid for my Nikon D70. So for me, using that perspective, I consider it a budget purchase. If you are looking for something below a certain $ point, you need to specify what that $ point is. If below $400, then the camera selection changes.
Budget also affects the lens selection. Example, I originally wanted the Hasselblad 180. But I did not want to pay the significant price premium over the 150. So I settled for the slightly shorter 150. A compromised based on cost. BTW, this is affordable (for me) USED prices $$$, not unaffordable NEW prices $,$$$.