How do you discover all the things you like/dislike about a new tool?
What do you rely on to make a reasonable evaluation of a new tool?
Feels like these two can answered at the same time.
Getting some hand-on time with it is the only path to truth. Doing a quick and dirty POC with a potential tool is going to give way more insights than an equivalent time spent reading documentation or evaluation articles somebody else wrote.
How do you know you’ve found “the one”?
Easy, or relatively low-friction acceptance from the team. You validate your findings, account for bias and if everybody else as hyped about it then there is something there.
What is the biggest turn-off when evaluating a new tool?
Some of these questions 
Tooling red flags:
- low or no community engagement, i.e. last contribution is 3+ months old, tons of GitHub issues with no answer;
- outdated, non-existing or bad documentation - not sure which is worse;
- pre-1.0 release (somewhat tolerable if there is a clear roadmap and vision);