What question / Issue comes first : Priority to select and determine course type and nature, or staff needing the Training?

Firstly, you need to determine whether your staff needs training or not. 

What I suggest you do is take a look at the performance of your different departments and see how their performance has varied from year to year. If a certain department has decreased in performance, then you can decide what type of training is most essential for that department, and based on that you can make your decision of whether or not training should be implemented. 

Technically speaking - Training Needs Analysis must come first, followed by suitable interventions and nomination decisions!

Analyse the performance of staff in work place and design training programs to suit the area staff are lack.