A company has an Apex process that makes multiple extensive database operations and web service...

This requirement specifies two critical constraints: the operations take a long time (likely exceeding synchronous CPU and timeout limits) and they must be performed sequentially.

Queueable Apex (Option D) is the optimal solution because it supports job chaining. Chaining allows one Queueable job to enqueue another Queueable job from its execute() method. This effectively creates a sequence where Job B only starts after Job A has successfully finished. Each job in the chain starts with a fresh set of governor limits, which is essential for "extensive database operations" and long-running callouts.

Option C (@future) is unsuitable because future methods cannot be chained; you cannot call one future method from another. Furthermore, the order in which multiple future methods execute is not guaranteed by the platform, violating the "sequential" requirement. Option A (Apex Scheduler) is intended for delayed or recurring tasks and is not designed for managing immediate sequential dependencies. Option B is a defensive coding practice but does not solve the underlying need to complete the work. Queueable Apex provides the programmatic control needed to manage complex, multi-step asynchronous workflows safely.