I would imagine a three piece would give you more room for error in comparison to the HD.A 2 piece has less moving parts so there would be less play.My HD I just purchased has no problems with razor play. I would get an HD. Look at first though and bring some razor blades too.
Razor: Merkur 38c, Merkur Slant,Merkur 39c Slant
Straights: Feather non-folding RG,DOVO "special" 6/8 tortoise,B&B LeGrelot LE
Blades: Derby Extra,Letterk pack,Feathers
Brush: Taylor Imitation badger
Shaving Soap: woodspritesoap.com organic "sand and fog" and "forest" soap, Miessence shaving gel
After shave: MIessence organic after shave balm
Used to own: Merkur HD razor,Merkur FUTUR,Muhle-Pinsel synthetic brush