There's nothing wrong with the Mossberg 500 except for having to remove the magazine tube from the receiver to pull maintenance on the magazine (a relatively frequent source of troubles on pumpguns). Mossberg cured that with the 590, it has a removeable magazine cap so the magazine tube can be cleaned straight through with much less trouble. Note the "relatively frequent" there, most new pumpguns don't have problems of any kind for years and years.
Chances are good it won't cause you any trouble unless you really get down'n'dirty with the gun, under normal use it should be OK. Given proper care and maintenance and usual levels of use the gun should still be working when you're taking your dirt nap. But if you plan on shooting 10,000 rounds a year at skeet or trap then you would likely want to get an 870... .
The combo package is a good deal, it gives you essentially everything you need at the same time as far as hardware is concerned. Just take your time learning the gun and be careful...
lpl/nc