If you know the scale length of your bass and what gauges are currently on it then I’d suggest doing this:
-
Adjust the tension of each string so that you get the best compromise of the factors you are looking for (finger AND pick AND slow tempo AND fast tempo). Don’t worry yet about what the strings are tuned to, just get the stings to feel the way you want them to.
-
Now get your tuner out and tune each string to the nearest half note. You aren’t trying to tune to EADG, you just want to get each string to the nearest natural, sharp or flat from where they are now.
-
Go to this calculator and input the info you have to determine the tension of each string. Now you have an idea of how much tension you prefer on each string, write them down.
-
Now change the tuning in the calculator to the tuning you intend to play and change the string gauges to give you tension close to what you got in step 3.
-
Order a custom set of strings.