you can use mesoporous materials (that have heigh specific area and can be reduced and oxidized)

The electrolyte depends with the elecctrode materials

i think you have to use Polymer electrolyte because which have satisfy your aim as well as it's not harmful your devise

Three class of electrolytes are there

Energy density E =1/2 .CV^2. so energy density is dependent on V and C. if you want to achieve, Use ionic liquid as an electrolyte. But it is costly.

Second choice is organic electrolyte ( ex. lithium percolate in propylene carbon) 

use aqueous electrolyte (Na2SO4...) limited potential is 1 V and organic electrolyte (LiClO4/CH3CN..) limited potentiel is more 2 V, you can use polymer electrolyte.