Do we create a rocket for the payload or the payload for the rocket?

Hey Striker, it's been a while! I used to make a payload first then build a simple 2 stage rocket around it, but as others have suggested I just have a rocket that can handle (almost) any payload. But if you want to be more realistic and more efficient then a family of rockets for diverse payloads would also work as Kell & Insanity suggested.

In real life or in game?

Especially in the real world designing a fully reusable system for a large variety of payloads would be the way to go, as you wouldnt have to dump most of the rockets potential if you launch a smaller payload.

In theory you could go either way. If you know exactly how much payload mass you have and precisely what orbit you want to put it in, you can build a rocket to perfectly match that specification and neither has more fuel capacity than it needs nor bigger engines than it needs. However this takes extra work for each payload (especially relevant in the real world where you cannot just tweak fuel tank sizes and engine parameters). Therefore it makes a lot more sense to build one rocket that can support a range of payload masses and orbits and simply calculate the fuel requirements for your particular payload/orbit profile.
When designing a rocket I usually design for maximum mass to LDO (Low Droo Orbit, aka parking orbit). Once have your rocket designed you should be able to calculate maximum payload masses for various orbits. If you want to launch a payload lighter than your maximum you can just adjust your fuel load accordingly.

I usually design a class of rockets that can handle different payloads.