So here is a QUICK rundown.
Primary vs atmosphere charger- the primary charger is the smaller of the two chargers. It does the majority of the work. When choosing a primary charger, you want a turbo that spools quickly and doesnt have a super tight exhaust housing so that drive pressures get high. The atmosphere charger feeds air to the primary charger. This charger needs to be sized appropriately to achieve a couple things: First, you dont want it to never spool, but you also dont want it running 40psi either (in a dd application). Most atmosphere chargers run along between 20 and 25 psi- just feeding a large volume of air through the primary.
Wastegating- You want to use a wastegate to keep the turbos (usually the primary charger) from overspeeding. Nitrous speeds chargers up which makes a bigger need for wastegates. You want to keep back pressure as close to boost pressure (1:1) as you can.
As for intercooling, depends how big you go. If you are running a big volume of air, you may want an aftermarket intercooler. The reason being is that if you are compressing air inside the intercooler, it is getting heated up. If your egts are high after that, you can add a stage of water after the primary before the intake manifold. Or, you can add a stage of nitrous at the track.
As for exhaust housing, that is all dependant on your charger setup/injectors/needs. The bigger the housing, the lower the egts, and the laggier it will be. Tighter housing= higher egts and lower spool up times.
Oil- Need oil going into the top of any turbo and draining out the bottom... as long as oil is flowing through you should be ok.