It definetly doesn't have to be a top line drum kit.
A nice Pearl, Yamaha, Tama, .... midrange kit will do.
Like mentioned before it's in the tuneing and often the lack of resonat heads.
Try a mesh (they look better than no head

)head on the kiks resonat side and a big pillow.
Tune the kick relatively high. You will be able to tune in the low end with a eq and a sub harmonic synth... this will keep the kick compact with impact and a good amount of lowend thump.
With toms there is the no head/mesh head way and the Pinstripe way (Sonor drumsets did come with Pinstripe on resonant side for some time).
With a Pinstripe head on the resonat side of the tom you will have a very dry tom sound no matter what you put on the batter side.
Pinstripe on resonant tom side will also lower the tom tone quiet a bit so the tom will sound fat...
On snare you might want to try a 14x6" tuned very low on both the batter and reso side. Use a good patch of gava on the batter side or even throw a pice of cloth like a kitchen towle on top.
Last but not least record the drumset in a totaly dead room... It has to suck the life out of the cymbals...