I use triple distilled as it has the broadest capabilities...ive not tried de ionised ..... Sure there will be some with better knowledge around who will guide you.
Here is a guide for what its worth...
Effectiveness of Distillation
Biological contaminants (viruses, bacteria, pyrogens, cysts):......Very Good
Dissolved gases (CO2, chlorine, radon):....................................Poor
Soluble organics (except VOC):............................................. ...Good
Particulates (sand, dust):............................................ .............Very Good
Soluble minerals (salts, hardness, iron, heavy metals):...............Very Good
Effectiveness of De-ionization
Biological contaminants (viruses, bacteria, pyrogens, cysts):.......Poor
Dissolved gases (CO2, chlorine, radon):.....................................Good
Soluble organics (charged ions only):........................................Good
Particulates (sand, dust, colloids):........................................ .....Poor
Soluble minerals (salts, hardness, iron, heavy metals):...............Outstanding
Effectiveness of Reverse-Osmosis Filtration
Biological contaminants (viruses, bacteria, pyrogens, cysts):......Very Good
Dissolved gases (chlorine only):............................................ ....Poor
Soluble organics (charged ions only):........................................Good
Particulates (sand, dust, colloids):........................................ .....Very good
Soluble minerals (salts, hardness, iron, heavy metals):...............Very Good
Effectiveness of Activated-Carbon Filtration
Biological contaminants (viruses, bacteria, pyrogens, cysts):........Poor
Dissolved gases (chlorine):....................................... .................Good
Dissolved organics (herbicides, pesticides, industrial solvents):....Outstanding
Particulates (sand, dust, colloids):........................................ ......Poor
Soluble minerals (salts, hardness, iron, heavy metals):.................Poor