I have to disagree in part with screamingdaisy, even though she makes an excellent point about choosing the right pickups. My disagreement isn't with the pickup advice, it's in the implication that the solution is "either/or". As in, "this is the culprit", "No, that is the culprit", "No, the real solution is this thing over here". People too commonly want to find a single convenient scapegoat for problems.
The truth is that
all of these things are factors in your final tone. The final tone that you hear is a product of many influences: the type of pick and how you're holding it, the pickup, the guitar cable, the kind of boost/OD you're using up front, the preamp tubes, the amp knob settings, the EQ in your effects loop, the power amp settings, the speakers/cab, etc.
A change in literally any
one of these things can affect your tone noticeably, and their collective influence on your tone may or may not be fully accounted for by a change to just one of them. For instance, in this example, let's say you go find and install a pickup with a lesser bass response, but a nice warm bark in the mids. If your cabinet is still too woofy or you still have your amp's bass knob maxed out, you're still going to sound like you're playing through a heavy quilted blanket. Does that mean that changing pickups doesn't affect your tone or isn't a wise idea? Of course not. It's a great idea. It just means that you may also have to adjust other factors as well until you find the desired tone.
Sometimes you have to learn the hard way....systematically going through each factor by trial and error. But I can tell you from experience that that can get expensive in a hurry. It's always wiser and cheaper to first learn
how all these things affect tone and to have a clear idea of the tone you're actually wanting. That way, you'll have a better chance of immediately identifying exactly what you need to change and by how much, and your chances of ultimately finding just the tone you're looking for go way up. Your bank account will thank you as well.