I would suggest a poly(ethylene glycol), poly(propylene glycol) or their copolymers. There are also used commercially for this purpose. If you need higher viscosity increase use poly(ethylene oxide), or poly(propylene oxide) – chemically same thing, but of higher molecular weights.
You should use polyvinyl alcohol, the one with 87-89 % hydrolysed (not the 99%). It adsorbs strongly at interfaces and can also increase the viscosity and it is commercially available in many different molecular weights.
most water-soluble polymers (synthetic and natural) are used as thickners, mainly the most powerfull ones : polyacrylamide (PAAm) and carboxymethyl cellulose (CMC). Regards