How to properly clean ECG and EOG artifact using Brainstorm for data recorded with EGI HydroCel GSN 128 1.0 system?

You need to detect the heartbeats and blinks from the ECG and EOG channels first. This is explained in the introduction tutorials: https://neuroimage.usc.edu/brainstorm/Tutorials/ArtifactsDetect

If you plan to use Brainstorm to process your EEG data, I recommend you start by following all the online introduction tutorials (section "Get started" on the tutorials page), at least until #19, and using the example dataset provided with the tutorials.
Then follow the advanced tutorial "EEG and Epilepsy" for additional information about EEG. This will teach you for example that we don't recommend using SSP for EEG, but rather ICA.
https://neuroimage.usc.edu/brainstorm/Tutorials
https://neuroimage.usc.edu/brainstorm/Tutorials/Epilepsy