Yup it is completely natural to be influenced by what you are listening to, and as others have said above it can be fun to experiment with different basses, buying used on the forum can keep costs down while you find the bass that suits you best.
A PJ just feels like home to me, I love the extra bit of definition that the J pick up brings.
Have fun experimenting, oh pick up an EQ pedal and your life might be nicer finding the tone in your head.