The type of coach that is best for your team will largely depend on your training type, and there are two differentr schools of thought.
One school holds that you should pick a coach to boost your strongest area (usually your trained area) even further, as it maximises the benefit of the coaching bonus.
The other school suggests that a coach to cover any weaknesses you may have in your weakest area
Neutral coaches are often suggested for use with balanced teams, which tend to be common only amongst the highest levels of hattrick.
To use defensive coaches as an example.
Some defence trainers or counter-attacking teams may prefer to enhance their defence ratings even further, whilst more attack-minded teams may prefer to use a defensive-minded coach to cover for weaker defenders.