I'm familiar with MH, but not Wunderfil, assuming they're relatively the same. Since bputty and MH accomplish the same task, I can't see a difference in outcome, but I think that more than merely filling alone, bputty adds a thin veneer. The big difference lies in application. And that would turn on how much detail your cabinets have. Applying a filler to detail with a brush would be far easier than a spackle blade, but I think that blading would be far easier on the flats than brushing a product of a melted peanut butter consistency. I've done quite a bit of filling details over the years with fingers as tools. The MH or Wunder may thin to a brush or rag app consistency. Maybe a combination of both.
There are pros and cons either way, and various work arounds. I would suggest that if you're committed to 86'ing the grain (for the new schoolers, 86 means gone or do away with), first be sure the painted grain is out of the question. And then experiment. With the amount of time and expense involved in such a project, some advanced fooling around and small expense is justified, and may just prove to reveal a more effective and efficient means to your end. See if a local kitchen place or similar have any dinged doors on the cheap to play around with.
As to primers, always a bonding primer for cabinets,
Zinsser BIN, pigmented shellac, superior bond, great stain blocker, excellent underbody for enamels, dries quickly but difficult to use if inexperienced, clean up with ammonia, since it sticks to glass you can eliminate sanding on smooth surfaces
Zinsser 123 or Inslx Stix, both latex bonding primers, easier app and great underbody, 123 about one hour recoat, Stix around three hours, least offensive odor, least universal stain blocker
Zinsser Cover Stain, oil based, great stain blocker, about two hour recoat, good but a lesser underbody of options, worst odor of options, clean up with thinner, sands powdery unlike other three
I've used them all over the years and any would serve, but the latex choices are probably best all around for what you need.