How would you choose which architecture you must implement in AWS? Which factors are chosen and which ones shouldn’t? What data is needed to have a wide decision?

Because of the scale enterprises and the software portfolio consisting of hundreds if not thousands of applications, most companies usually end up deploying every imaginable architecture. Ideally everything will be SaaS/cloud-native/microservices-based, and enterprises that are "cloudy" have a preference tree of application architectures, with lift'n'shifted monolithic systems being the least desired. But companies have to deal with a lot of apps in the middle, e.g. partially refactored, and also vendor applications that are only half-way cloudy. 

More important than any one architecture is the organizational structure supporting cloud/AWS. A centralized team (aka Cloud COE) can work with many application teams and guide each to a more optimized solution or architecture. They'll also handle the cloud vendor(s), assist with training, EA, etc. 

What data will be stored? What data is running through? Etc. For example healthcare l, government, financial have different criteria and may need private cloud. Get with AWS professional services for support and look at the blueprints but the company are the ultimate decision maker and liable. Pay close attention to share responsibility matrix