Well the good news is that most derringers are extremely reliable, they have very simple actions and are less suseptible to crud from fireing entering the action due to no path for it to follow,(note: you WILL get some, but not like a revolver).
As to cleaning, personally I clean all of my guns after shooting, anything from 1 round to 100 rounds (doesn't matter) I guess I am just anal about that, but if you work with what ever you are comfortable with you will be ok.
I checked the "winchester ballistics chart" on line, and the minimal list of numbers for 158gr. bullets are as follows:
.38spl (standard)=755 fps at the muzzle
.38spl. +p=890 fps at the muzzle
.357 mag.=1235 fps at the muzzle
These numbers are from test barrels, your numbers will be different.
It should be noted that using +p ammo in a gun that is not rated for +p will accelerate wear, but with minimal use of +p, you should be able to practice with standard loads for many years, the .38spl derringer I own has got to be 20 something years old and has many hundreds of shots fired, other than the finish being worn off there are no signs of my not having it for the rest of my life.