Both approaches are valid; the right choice depends on commercial priorities and budget.
Registering in multiple countries simultaneously establishes the same priority date in all of them, which prevents third parties from filing first in any designated market. This is the stronger position if you are about to launch in those markets or have reason to believe competitors might file before you.
A phased approach, starting with the highest-priority markets and adding others over time, is more cost-efficient and practical for businesses with limited budgets. The risk is that a third party files in a market before you register there; in first-to-file jurisdictions, they would then hold the rights in that country.