I won't get into the specifics of an 870, since those guns generally fit me pretty well and there are others here with far more experience making modifications. I do, however, have a fair bit of experience with modifying other stocks for fit. First of all, if you have any woodworking or mechanical skills at all, it's not a bad project. Second, it's an 870. Even if you totally botch it, replacement stocks are readily available and relatively affordable.
All this being said, having a gun fit to you is an experience I think every shotgunner should go through at least once. The prices can range from maybe $100 for a change of LOP, pitch and a recoil pad to over $1000 for a true custom fitting and a stock handmade to your dimensions.
Most importantly, I'd take it slow and make one change at a time. If you change more than one thing at a time, then you can end up not knowing what to alter if problems occur.
IMO, the first thing to get right is LOP. Coupled with this, you want to get the pitch* correct. This is also an ideal time to add a premium recoil pad (Pachmyar Decelerator, Kick-Eez, Limbsaver, etc...).
Since LOP and pitch both have an effect upon drop, make sure that you pattern it and shoot it a bit at this stage to get an idea if you need to alter the drop. If, when you pattern the gun, it is shooting low, you'll want to decrease the amount of drop. On the other hand, if it's patterning high, increase drop. Work in small increments, since it is easy to remove wood, but difficult to replace it.
I believe that Dave McCracken has posted in the past about using shims between the receiver and stock in order to change the cast (and probably the drop as well).
* Pitch is the angle of the cut at the rear of the stock. Depending upon the configuration of the shooter and the gun, it may be necessary to either increase or decrease that angle in order to provide optimum contact in the shoulder pocket. For example, my Winchester 1300 Defender naturally pointed quite high for me. When I cut the stock down a bit, I removed more material from the toe of the stock than the heel, and now it points exactly right.