My defaults
What I actually reach for, and the single most common error in method selection.
The comparison table gives you the shape. Here is what I actually reach for, on the understanding that any of these can be overturned by a specific constraint.
Oracle source, model carrying forward, weekend window available. Logical migration with Data Pump, offline. It is simple to operate, easy to validate and the failure modes are well understood. Teams reach past it for TTS more often than they should, because TTS sounds more sophisticated and because the data-movement time looks better on a slide. If a Data Pump export, transfer, import and validation fit inside your window with a comfortable margin, stop looking.
Oracle source, and the above does not fit the window. Now compare TTS against logical-plus-replication. TTS is the stronger choice when the physical design is genuinely being preserved and the source can tolerate a controlled read-only period. Logical-plus-replication is the stronger choice when you need object-level selection, when the target design differs, or when the business will not accept a hard read-only period on the source at all.
Oracle source, but the target model is substantially different. Extract, land and load, or rebuild. Do not use a physical method to move a model you intend to replace; you will pay for the physical fidelity twice.
Non-Oracle relational source. Extract, land and load for the data. The data movement is the straightforward part — see converting the code, which is where the project actually lives.
Hadoop or Hive source. Extract, land and load, usually with the landing zone as the destination for a meaningful proportion of the data rather than a waypoint. See Hadoop and Hive sources.
The single most common error I see is choosing the method before deciding what the target design is. Method follows design, not the other way round.