How typical is it for cancer to spread to different parts of the brain?

Depends on tumor : Type. Some tumors spread to brain more often than others, e.g., lung cancer, melanoma spread to brain more often than colon cancer.

Although varies: Most common secondary metastatic brain tumors, primary from lungs, breasts, skin, kidney, gastrointestinal tract. Some can present with bleeding, especially melanoma and lung cancers. Although the spread may be mediated via blood vessel flow, and statistically may be more often on left brain, this is so variable, that statistics only minimal correlations.