As you mention it is similar in principle to choosing any off-the-shelf product (requirements, evaluation, short-list, trial, etc).
As to [a]ny links or perhaps suggested processes?:
For software in general How to Choose Business Software and How to Choose Software, both offer different styles. The first is a common step-by-step 10 item list with some additional Tips, the second is one man's opinion in 3 paragraphs followed by 2 marketing his own. The second, however, is more closely related to game development because it focuses on productivity exclusively.
As for development specific there is the 15 Most Important Considerations when Choosing a Web Development Framework and Choosing the Right Java Web Development Framework. The first here applies to any framework (except for the question of which JavaScript library is included), which is essentially what a game engine is. The second provides more of a magazine Top 10 ranking process.
Finally, I just found How to Choose a Mobile Game Engine, but it is not yet published.