Rook Ares' answer is a bit dated and inacurrate unfortunately.

Here's the low-down as of Dominion:

The 3 short range ammo are:

EMP -- Mostly EM Phased Plasma -- Mostly Thermal Fusion -- Mostly Explosive

All 3 deal the same raw damage. This is new in Dominion.

Barrage is the T2 long-range ammo for autocannons only. It is awesome. It does have tracking penalty so should not be used at short range. Damage is a mix of Kinetic and Explosive.

For T1 ships, the basic idea is:

Fusion against armor tanks EMP against shield tanks Phased Plasma is an OK compromise

Barrage is special in that at range beyond about half of Fusion/EMP's falloff it deals more damage and does so until the target is much further away. In a rifter with 200mm AC IIs, from about 5km for fusion and 6km for emp.

For T2 ships things get complicated:

Gallente & Caldari: Fusion & EMP, they are the two lowest resists. EMP has an edge for Caldari and Fusion for Gallente but it's quite common for a Gallente to have a T2 explosive hardener and the EMP is best. Similarly for Caldari.

Amarr: Thermal or EM. Forget about Explosive.

Minmatar: Kinetic is best followed by Explosive.

Now in practice Minmatar ships are hard to predict. Hurricanes, sometimes even Ruptures, are just as likely to armor or shield tank. Gallente BCs, same idea, shield tank + neutrons on Brutix, passive shield tank on Myrmidons.