Ususally, guns are most powerful when hit from a close distance, and the probability of hitting is also highest when close. This means, though one has set high convergence range, and all the bullets may converge and hit the target, it is significantly weaker and chances of damaging the target plane is low.
Since setting high convergence ranges is rarely efficient due to:
1) Weak power from distance
2) Low probability of hitting the target
3) Lot of wasted ammo
4) Target plane can easily maneuver out of way
.. This naturally suggests the tactics the real aces used. Get in close, then go closer. Set the convergence at low range. Most usually people set convergence ranges around 200~400 yards. And as you have questioned, different types of guns and ammo require different settings.
The standard USAAF weapon .50 Cal Machine gun is known for its high velocity and accuracy. When set at around 250~350 yards, it can hit close targets from 200 yard range to far targets up to about 500~700 yards. In case of Luftwaffe MG131 13mm machine guns, the rate of velocity is high but accuracy is lower than .50 Cals. Even at convergence, it is not much effective over 500 yards - thus, it should be setted between 200~250 yards(firing range should be not over 300 yards for best effect).
In theory, cannons have lower velocity than machine guns, and the shells - due to its heavier weight - drop more. This means you should set the cannon range slightly higher(about 25~50 yards) to compensate for the difference in drop rates. But in actual practice, the drop rate does not make much difference when you fire under 300 yard range. And since cannons have low ammo, nobody would want to waste it in long range tracking shots anyway -> this means most of the times, cannon shells are fired at a close range where the drop rates don't make much difference. So, there is no real need to set cannons and MGs differently. (But then again, there are those C-Hogs and N1K2-Js spraying at anything within 1.0 range.. but..
)
And, another thing, setting different convergence in individual guns do make some sort of difference at hitting the target. For instance, P-47s with 4 pairs of .50 MGs... if you set the innermost pair at 200, than proceed with 25 convergence apart.. so the guns are set 200, 225, 250, 275 .. in this case, the bullets are more spread out, therefore, chances of hitting the target are high - but the power will be weak. If you set all 8 guns at 200, the chance of hitting is low, but you'll have maximum power. You could set convergene at 'hybrid'.. inner two pairs at 225, outer two pairs at 250.. experiment with it and see which suits you best. But if you prefer shooting decisive and powerful bursts at real close range, of course, all guns set to about 200 yards is the best.
So to add it all up,
If you fly a USAAF plane, set the convergence between 250 and 350. If you fly a RAF plane, set it at about 250~275. Luftwaffe planes should have it at 200 or 225. Whatever the plane, the convergence should not go higher than 350.
