Do you want to customize it, or just make it work better? I am a fan of the basic format, so I have nothing to say about customizing it.
To do a functional tune up: Completely disassemble the shotgun and give it a very thorough cleaning (leave the trigger group intact, but clean and degrease it thoroughly). DO NOT yet lube it. Reassemble the shotgun, and cycle and dry fire the p1$$ out of it (thousands of cycles, while watching a movie or something like that). Doing this dry (without lube) accelerates the wear-in process. If you have dummy rounds, cycle them as well (easy to make using fired hulls and 3/4" dowel).
Disassemble the firearm again, and give it another cleaning. You should be able to clearly see where it is wearing (finish is worn off). You can stone and polish those areas to great effect. While you're at it, polish the chamber and barrel as described above.
Lube, reassemble, and you will have a MUCH smoother feeling shotgun.
Then use it for a range session or two, and you will quickly learn which sharp edges can be smoothed for a better feeling shotgun.
Or just shoot it and shoot it some more.

The 870 design wears in very, very nicely.