Electronic – Digital oscilloscope minimal sample rate to capture SPI data going at 500 kHz

It looks like the test is designed to be done as a loopback test (i.e. with the SIMO/SOMI pin shorted)
If you don't have them shorted, you won't see anything on the SIMO line unless you have a signal input from elsewhere.
SIMO = Slave In Master Out
SOMI = Slave Out Master In
I'm assuming the beagleboard sets itself up as a SPI slave, hence the pin names (more commonly MISO and MOSI)

As far as the scope settings go, x10 for the probe is best as it adds the lowest capacitance load to the line under test (means you can see higher frequencies)

For the timebase and Vdiv, just set things up as needed on the fly. 2us and 1V/div sounds fine to start with. You would often set the Vdiv to a sensible value for the bus voltage to get the signal to fill a large portion of the screen.

Then adjust the timebase in/out when you want to focus on different things, e.g. smaller if you want to check the risetime of the signal, ringing or transients, larger if you want to see more than one byte or stuff like power supply interference.
You will quickly find you are twiddling the knobs constantly when debugging, so don't worry too much about initial settings.

To measure a digital signal the Nyquist-Shannon theorem says you need a scope with a sampling rate at the very least twice as fast as the frequency of the signal you are sampling. An USB 2.0 bus is capable of 480Mbit/s, which means you would need a scope capable of AT LEAST 1GS/s (a billion samples per second) to be able to resolve individual bits. You have the wrong equipment for the job.