1st gen cummins - uses mechanical rotary pump - can be made to make decent power for little money. Fuel mileage is decent. Early ones did not have the intercooler I can't remember the first year for the intercooled dodges.
Everything below was intercooled from the get go.
2nd gen cummins - uses mechanical inline pump - often referred to as a P-Pump. Can be made to make insane power for little money. typically these are known for the best MPG.
Both of these engine share a lot of parts and there really isn't much difference between then other than the fuel system.
Both of these only need one wire to run = fuel shut off solenoid power.
The 2nd gen also has the 24V engines which started in late 98. These require the use of a ECM to control the rotary pump VP44. These can be made to make decent or insane power but costs a bit more money to do it because you have to actually purchase all the items to increase their power. But this brings on the ability to at the flip of a switch or press of a button increase the power setting or lower them. These typically get decent mileage. This engine still has mechanical injectors. The VP44 has gotten quite the bad name because they tend to fail in stock form. I have heard a lot of reasons why but the one that seems to come up a lot is that because the pump is lubed and cooled by the fuel that if your supply pressure or volume drops then it's pretty much downhill from there.
Next in line is the Common rail fuel system. In this application they feed fuel to all the injectors at all times then open the injectors electrically to control the fuel. These are typically the quietest of all the Cummins engines in that they don't rattle as much. That was a big selling point for them. Again this engine will require the use of an ECM to control it. Fuel mileage is decent and again just like with the VP44 series engines you can have anything from decent to insane power levels. but it costs money.
Now they have 6.7l which I don't know alot about other than it's computer controlled and seems to be proving out to be as reliable as all the previous engines.