First of all, welcome to the T&TH site. This is a great place with lots of good folks who are very helpful. congratulations on your new Remington 11-87. It's a great gun. I've been shooting them for many years and currently shoot 2 with the ShurShot stocks. I know you'll really enjoy that gun.
I'd encourage you to "deep clean" the barrel. It's best to do that prior to shooting but you can do it at any time. It will really help your patterning. The article "Cleaning a Shotgun Barrel" http://allaboutshooting.com/article_info.php?articles_id=282
has some guidelines that you may find helpful.
In my experience, the 3" Winchester Xtended Range H-Density shell with 1.75 oz. of #6 shot, the 3" Winchester HV shell with 1.75 oz. of #6 lead shot and the 3" Hevi-13 "Bronze" shell with 2 oz. of #6 shot are all excellent shotshells with the 11-87.
There are several good turkey chokes that will work well with your 11-87, again in my experience. I've had great results for the last several years with the 3 shotshells that I've mentioned and the SSX Turkey Choke http://allaboutshooting.com/product_info.php?cPath=23&products_id=74
That choke is rated for all lead and tungsten-based shot, has excellent "internals" and is very reasonably priced for a premium quality turkey choke.
No matter which choke or shell you choose, I wish you the best with your new gun. If I can be of any help, just let me know and I'll do all that I can to be of assistance.