I have a 12 g. Remington 11-87  and I wonder what choke youd recommend?  what barrel length?  thinking 18.5 barrel or 21, with full choke.  any recommendations?

Chokes and to a lesser degree bbl length, really depend on your anticipated range(s).  A 21" bbl with a modified - full is a good place to start...

My buddy up in the Alaska range uses a turkey choke i gave him in his Benelli M-1 Super 90 for coyotes and the occasional wolf. Tight pattern at longer range.

I haven't killed a coyote with it yet, but my Benelli M2 Tactical is set up with a Carlson's extended extra full turkey choke.  Patterns are tight enough with 3" Long Beard #4's out to 60 yards.  I would think any 3" heavy load of #2-#5 shot would work. Maybe #4 buck shot?

Every shotgun is different, you;ll have to try some on paper to figure out what your gun likes. I use a Carlson's Dead Coyote choke with copper plated BB up to #4 buck with good results.

I use #4 buckshot, you need to pattern your gun/chokes with your load. Mine patterns best with my modified choke with some loads. With my handloaded #4 buck my turkey choke patterns the best.

With larger pellets (often used for larger game than birds) a full choke tube may actually provide a looser - wider pattern than a modified.

Pattern your shotgun to see how it shoots with what you shoot...

BIGGER_HAMMER

Patternmaster EXT choke or carlsons modified with lead buckshot, or A dead coyote choke with dead coyote loads.

The smallest shot I would shoot in a 3" load would be lead BB, in a plated pellet and well buffered.  I've shot dozens of fox and coyotes with winchester lead BB, through a patternmaster choke inside 40 yards.  I don't prefer BB for coyote, but it's great for fox.  for 30-70 yards, and targeting coyotes specifically, buckshot or dead coyote.  the energy retention of the tungsten dead coyote loads gives sufficient penetration on coyotes out past ranges that most gun/choke combos can hold a pattern together.  Nothing worse than tracking a yote for 2 or 3 miles after you only put one pellet in it.
Hornady superformance buckshot used to be my go-to load, but I really am starting to like the federal buckshot loads with the flight control wads.  they are pretty sensitive to chokes though, and I wish they made a flight control load in 3.5" of #1 buck.

For woodland coyote work I use a benelli m2 with a 21" barrel with carlson choke and dead coyote loads.

Mossberg Tactical Turkey. I believe it's a 535.

4 Buck and turkey choke for me.

If making them dead is your primary objective, slugs will pound them at much greater distances.

Picking them off at 110 yards is still a good option to keep available in thick woods.

Cylinder bore and a breneke black magic will do just fine

Hey thanks.  got the Carlson "dead coyote" choke.  Using number 4 shot and 3 inch loads.  I think I'm there!

OP, you need #4 Buck not #4 shot.... #4 shot is for birds.

Got this one a couple days ago.

The shorter barrel will be more maneuverable but will reduce your range some, I always want to extend my range as far as possible, I just a Truglow Gobble Stopper choke and its holds a pretty tight pattern, check out federal #4 Buck 41 pellets in a 3" shell-bad stuff