I guess people use HCl solutions, since PdCl2 dissolves in conc. HCl forming [PdCl4]2- ions. If you want it in a simple equation: PdCl2 + 2 HCl = H2[PdCl4]. If you do electrodeposition with such a solution there is nothing but Pd2+ Cl- and H+ in it, no other "rubbish". This give probably the best results.
Another important point is, that H2SO4 and HClO4 are not only acids but also oxidising agents! Thus, you will not be able to generate elemental Pd in such solutions. Pd will be oxidised back to Pd2+. This will not happen in HCl.