o2 Oxygen Sensors

What do these o2 sensor things do? 

They measure the amount of Oxygen in your exhaust and convert that into an electrical signal that the vehicle's computer can understand.  That way the ECM/PCM can automatically adjust the fuel based on changing factors.  Most common configuration is 2 upstream sensors, one for each side of the engine, and 1 downstream sensor to check the function of the catalytic converter.

The upstream sensors determine how the engine runs in closed loop mode, they are the ones that monitor the air to fuel ratio and affect engine performance.  They do not function properly when cold, they are ignored during engine startup until they warm up.  Newer ones have a heating circuit so that they can start working sooner.

The downstream sensor, the one beyond the catalytic converter is only there to monitor the function of the cat, it does not affect the running of the engine at all.

Which is Bank 1 Sensor 2? 

Bank one always designates the side of the engine with cylinder number 1 on it.  Bank 2 is always the side of the engine that has cylinder number 2 on it.  

Most of our vans will have 3 sensors, B1S1 on the upstream drivers side, B2S1 on the upstream passenger side, and then B1S2 beyond the catalytic converter.

Here is a diagram that should make it easier to understand.

What brand o2 sensor should I buy for my Astro/Safari van? 

I'm not a this brand or that brand kind of guy.  In fact some of the aftermarket stuff is better than the OEM stuff that was originally installed.  In this case however, my only advice is that for o2 sensors, stay away from Bosch.  There are numerous years where these problems have been reported so I would just skip Bosch o2 sensors for our vans 100%.