Hi Jonny,
I would first suggest that you set the neck tension / truss rod, before relying on the bridge adjustment. There will be plenty on Google about that - and I found the Dan Erlewine book ' How To Make Your Guitar Play Great' an interesting and instructional read, even after I had started 'dabbling' with my own guitars.
My preference is 1/32 " = 0.8mm at the 12th fret for my Jazz guitar - and as close as possible to that ( usually 3/64" = 1.2 mm ) on guitars where I need to bend the strings a lot. For me , this equates to
relaxed playing - as opposed to overt speed, although relaxed does equate to improved dexterity for me . Being relaxed also 'feeds' the way in which I like to play.
I prefer both low and high 'E' to be as low as possible, without fret rattle at any position - at medium pressure of pick attack . I was surprised , for example - that Twinfan ( although a fast player when needed ) - likes a higher action than I would, even on the very highest quality guitars. I was also surprised to find out that one of my own guitar heros ( Larry Carlton ) likes 1/16" = 1-6 mm or higher at his 12th fret, and he is considered a somewhat laconic player.
Sometimes a cheap far east copy ( see my avatar ) sets up lower and slinkier - ( with or without fret leveling ) than some high $ American guitars. I mention that last point , not out of inverted snobbery - but rather to emphasise that good things can be acheived - even on a guitar that one might initially expect far less of.
I hope things turn out good for your own set-up. :)
(* Edit *)
I forgot to mention, that when in the final stages of setting a guitar up, I am constantly going between the last fraction of truss rod adjustment and bridge height adjustment ( whilst constantly re-tuning to re-check I am setting the whole lot up against the 'working' tension ) -
and letting it 'settle in' overnight. As a result , the 'patient' often sits with the truss rod key inserted on the guitar stand for 2-3 days , before 'going to press'.
This brinkmanship has often yeilded great results - and has (for me ) been well worth the extra time and care taken . Your mileage may vary - as an O.C.D approach does not work for everyone ...
