the basic need for this kind of setup is cooling of the most likely fully floating bearing assembly, and not lubrication. of course the bearing has to be lubricated, but as long as you make sure that a sufficient flow of oil is maintained at all times, there is not much reason for worry since the bearings are not heavily loaded.
sufficient cooling is achieved by using the thinnest oil possible and hence the use of ATF in certain applications (about SAE5W-20). ATF's also have good thermal and oxidation stability and some detergency. however, if there is a appreciable leakage of exhaust gases into the oil the detergency and dispersancy might not be sufficient and a low viscosity/high viscosity index engine oil might be a better choice.
one other thing to consider is what happens when you turn the engine off. in that situation the turbo might spin for a couple of seconds with no load - and thus pumping nearly all the oil out. all the heat that is still left in the turboassembly will then be "soaked up" into just very little oil and this might cause the oil to crack and generate heavy carbon deposits on the inner surfaces of the bearing assembly. to prevent the effect of this heatsoak effectively it is wise to either have the engine idle for a minute or so before shutting down or, when you use an electric pump, have it equipped with a timing device that lets the pump run for a certain time after engine shutdown - where even the amount of running time after shutdown might be governed by the temperature of the oil that is coming out of the turbo.
my personal preference for this type of application would be a low viscosity engine oil - it has the necessary detergent/dispersancy characteristics and can withstand higher temperatures then ATF. i would not use a synthetic aviation type of oil - they are much more difficult to obtain and depending on the type of synthetic used might require that the seals in the turbo have to be changed because they are not compatible with the synthetic used.