There is no best voting method.
You can always find a specific situation where a given voting method produces the wrong result. However, whereas in general there is no perfect voting method, in practice there are voting methods that can be worse or better for you and your organization.
Here are a few suggestions to guide you in the forest of voting methods. Take them with a grain of salt and judge for yourself, which is best in your specific situation.
Questions and answers to find the Best Voting Method
Q: I need to take a decision concerning a very small number of choices (2-3)
A: consider plain Single Preference voting
Q: I need to choose between a moderate number of choices and I want a simple and solid method…
A: consider Approval method
Q: I need to choose between a large number of choices; my voters have no reasons to be insincere…
A: consider Borda method
Q: My voters are familiar with Runoff method and would like to avoid voting twice…
A: consider Instant Runoff method
Q: I need to choose between a large number of choices; I want to be as robust as possible against insincere votes…
A: consider Condorcet method
In most situations the simplest voting methods are the best solution: so consider plain Single Preference voting and Multiple Preference approval before any other method. Sometimes you may want to use more than a single voting method, and may want to study the robustness of a result against different voting methods.
In the case of small committees with highly skilled voters, one may consider using sophisticated methods. In this case Condorcet is usually a good choice. It may easily produce ties, however, so it may be a good idea to confront the result with the Borda method results, which are much less likely to end up in a tie.