There are a lot of guides about the pickup height for singlecoil and humbucker pickups but there is very little guideline on active pickups. I have had my pickups in the default position since I bought my guitar (Ibanez RGA) but they have slowly lowered over time and I think I should find out some more detail about tone before changing them. I play a variety of guitar styles: Metal, Funk and Blues mainly. Are there any heights that work for all or which are best for certain ones. I need the best sound quality too and the right balance of high/low frequencies. Thanks
There is no absolute answer to this question. In reality any pickup height can work for any style of playing. What will change with different pickup heights is the tone colour, for two principal reasons:
The closer the pickup is to the strings, the bigger the induced voltage will be for a given string vibration. This will increase pickup sensitivity as well as improving the signal to noise ratio.
The closer the pickup is to the string the more the magnetic field from the pickup will distort the free vibration of the string. This will cause (probably unwanted) filtering effects as certain harmonics will be damped out of the vibration. The magnetic attraction will also decrease the sustain. If you place the pickup too close to the string it will eventually impede the vibration of the string almost completely.
Both of these points apply independently from the fact that you have an active pickup. Active pickups still use magnets and coils just like other pickups, so all of the points you have read elsewhere about pickup height will also equally apply to active pickups. The best advice is just to go ahead and try out some changes until you get a feel for a sound you like.
As stated, your question asks for the "best" sound quality and I think this makes the question too subjective to give a definitive answer.