After the feedback I have tried a few different textures to see which one will work the best. These are the ones I have now:
I have used concrete, paper, ice, fingerprints and just for the fun of it an x-ray image.
I got some feedback on these and at the moment nr 2 and 7 are the favorites. Though the fingerprint on nr 7 needs to be a bit less bright as it distracts from the text.
EDIT: I made the fingerprint less bright and asked people again what they thought, and thins time nr 7 outvoted nr 2. I also like nr 7 as it adds this ‘crime vibe’ that I think was lacking before.