My original 870 was (still is) a police trade-in with a 20" bead sighted CYL barrel. It did almost _too_ well on flushing quail over a dog- they didn't have a chance, hardly. I also used an old ex-GI Savage 720 riot gun with an 18" CYL bore that my grandfather had bought surplus, same deal only moreso, I only took that one out once. See
http://ugca.org/03mar/savage.htm for more info on that one, as much collector interest as there is in those now it won't be afield any more.
The IC choke will give you a bit more range, a bit tighter patterns and a great deal more overall versatility. I like the fixed choke idea better for a working (HD/security/serious/social/tactical whatever) shotgun, and the IC is no disadvantage unless you want to tweak absolute maximum performance out of long range buckshot loads or hunt turkeys. With the relatively new Hevi-Shot buckshot there isn't much need for tweaking and a fixed choke is a better option for shooting it IMHO. For turkeys, choke tubes are the way to go. There is no real disadvantage to a shorter barrel for a practiced wingshooter, especially on upland game, so the 20" barrel should be no problem.
The last- well, let's say most recent 'cause it won't likely be the last- Cinderella 870 (used, that is) I bought off the rack was an Express Turkey Gun with a 21" vent rib barrel and twin beads, set up from the factory for RemChoke tubes. If I were limited to a one gun/one barrel deal, this would be it, especially if I could get an assortment of tubes. It seems to me the best compromise overall. The fact this one was $145 out the door, with a set of aftermarket sling swivels installed, certainly didn't hurt my feelings either. It was one of the older Express guns, no dimples in the magazine tube and an aluminum trigger plate. Looked as if the previous owner used a lot of bug repellent or the like while hunting the big birds, the stock finish was dissolved wherever hands had touched the wood, it was ugly and sold cheap but it was mechanically solid as a rock.
I wouldn't worry too much about _having_ to have police gun, there really honestly isn't that much difference (except price, if you buy new). A good used Wingmaster and a spare barrel won't likely cost any more than a new 870P, given judicious shopping, and it should cost even less for a good used Express gun of the older (pre-dimple, pre-plastic trigger plate) vintage. The only marked 870P I have was bought used (as a retirement present to self a few months ago) as a PD turn-in and you are right, it has a noticably heavier trigger pull. It is going to get tuned eventually, but my wizard will get that task, it's not a DIY job, IMO.
I got the forcing cone done in the retired 870P (18" IC bead sighted barrel, factory magazine extension, blue/walnut) at Colonial while I was home near Selma, AL for the week of Christmas, cost $45 and Red Lyles got it done for me while I was running errands in town. Dunno how much you can get it done for other places.
hth,
lpl/nc