How does an airline decide on an engine?
I think you are answering your own question. It all boils down to money. Every factor of the aircraft buying process will be driven by money. They are, after all, a business. Some decision driving factors may include:


The acquisition cost.
The operating cost.
Fuel efficiency. Fuel costs the airline money
The reliability. Down time for the aircraft loses the airline money.
The liability. Is it going to breakdown midflight and cause death and lawsuits?
Manufacturer support. Will they get help if problems arise?
Is their an adequate supply chain of parts?
Airline’s specific history with that engine.
Does the airline already have mechanics certified and experienced for that engine?
Do they already have parts and spares of that engine?
It is easier to maintain only one type/model of engine across their fleet than several.
Tax incentives.
National loyalty for some airlines.
Brand loyalty for other airlines.
Kickbacks
TBO. Maintenance costs money.
Core resale value.
Possible advertisement opportunity.
Contractual agreements.
Politics (both internal and external)
Etc.