These days most H1.2 treatments are with boron salts. These are very low toxicity preservatives and should pose few problems when used for indoor furniture, although it would be a good idea to ensure there is either a paint or other surface finish on the furniture so that there is no direct skin contact with the treatment.
H3.1 treatments are usually organic solvent treatments (eg. LOSP). These can cause some dermatitis-like problems when freshly treated timber is handled, particularly if a lot of residual solvent remains. They also have a fairly pungent aromatic smell which may take a while to dissipate from the treated timber. Again, painting of the timber would be recommended once all the solvent has evaporated.
H1.2 boron treatment would be the preferable option.