EXP is granted from a variety of actions (curing/taking damage/dealing damage/enfeebling/enhancing/etc) so
using a job which can do most of these is recommended (e.g. /dnc).
There are
caps on each category as well as a "hard cap" which cannot be exceeded. This hard cap is determined by your
Medal Rank, and increases every minute. http://wiki.ffxiclopedia.org/wiki/Campaign:_Experience_Point_Calculation_Guide#Time_and_Medal_Total_Caps
For example, a 3 minute battle as Sterling Star (70xp/min) grants a maximum of 210exp. Allied Notes is half of this, so 105. However, if you were to exceed this cap, all isn't lost yet, since your
Allied Notes will still increase but your EXP will not, this can be easily seen if your Allied Notes is greater than half of your EXP (e.g. 210exp and 160AN). The maximum cap for Allied Notes is EXP+4 (e.g. 210exp and 214AN).
As for choosing the best job, I advise you just go out there and kill stuff, bearing in mind the caps for categories, and see if your AN at the end is greater than half of your EXP. If it is, you're doing it right.
The best way to get allied notes though is by
Campaign Ops (1k-2k per go if you choose your op/star ranking correctly).