I would agree to saving up for a good semi-auto, specifically a nice ( used ) Berretta 1301 tac. The resources on the various P&S sites and Modcasts pretty much lay out the reasons why. I would also recommend watching "The Guage" Modcast episode....twice. P&S has some of the best shotgun SME's out there..
Having said that, there are a couple of things I look for when buying a used Remington 870 (and I don't know much about the other brands).
I would suggest researching the differences in 870's....870 Express, 870 Wingmasters, 870 Police models, etc.
As far as inspecting it..
First thing I do is pop off the magazine cap (or extension). I look inside to see :
1. If the tube has dimples or not, and if not.....were they removed in some funky form or fashion.
2. Is there any rust in the tube or the spring?
3. Is the tube still straight?
4. Will the follower run down the tube smoothly with just gravity...without snagging up or stopping anywhere?
Next I would look to see if the lifter has the Flex-tab modification to it or not. Is the action smoooooth?
Can you take to barrel off relatively easy? I have found that a bound up barrel is usually a sign of trouble.
Take a look through the barrel for any pitting or irregularities.
Will the action bars and action come out relatively easy?
Does it have a good, firm trigger pull?
I know I'm forgetting some things...
As far as basic upgrades....
To start with, I would recommend a Vang Comp safety and follower ($40). Replacing the magazine spring is never a bad thing ($10).
If you want a shotgun with an extended magazine, I would suggest buying one that is already set up for it, or already has one. Trying to remove the dimples without messing up the tube can turn into a real pain in the ass sometimes.
If you want a light, do some research into what works for people. I recommend buying the older Surefire fore-ends made for the 870. If you are lucky, you can snag one one fleabay for a little over 100.
A sling is a good idea, one point or two....depends on you.
Hope it might help....worth what ya' paid for it.
Good luck!