Welcome to the Turkey & Turkey Hunting site. I'm sure you'll enjoy it here and find lots of helpful folks who will be pleased to be of assistance.
Both my wife Doris and I shoot several Remington shotguns, including 870's. I'd make just a couple of observations and suggestions for you to consider.
Even though your gun has a 3.5" chamber, you may want to consider shooting 3" shells. For many shooters, the 3" shell witll pattern better than the 3.5" shell, it costs less and has much less recoil. The 3.5" shell certain has more pellets and may put more holes in the paper but in many cases, you'll have a more even consistent pattern with the 3" shell.
Remington shotguns use the magazine cap to help hold the barrel in the receiver and to keep it from moving at the critical instant of ignition of the powder. It's very important that the cap is very tight and is in the same position each time. Otherwise, the center core of your pattern can move, up to 8" in some of my Remington guns. I recommend that you hand tighten that cap and then, using padded pliers, tighten 4 more clicks and then mark the cap and the barrel band, so that you can get it back in the same position each time you take your gun down and reassemble it.
I'd also recommend that you really clean that barrel prior to shooting it for the first time. Some barrels are really sensitive and will only shoot at their best when very clean. Some barrels like to be a bit dirty and the only way to find out, is to start with a "squeaky clean" barrel and shoot it a bit at a patterning board, without cleaning between shots, to see what your gun likes.
I wrote an article, "Cleaning a Shotgun Barrel" that outlines the procedure I use and recommend. It involves using a good cleaner, a new or excellent condition good brass/bronze brush and a good bit of scrubbing. I can direct you to that article if you'd like.
There are several good turkey chokes. I try to shoot them all, in every exit diameter and with all the turkey loads on the market. A good bit depends upon the turkey load that you use. I try to make recommendations that will yield the best patterns at the least expense.
I'll make one and doubtless you'll receive many others. One combination that will give you excellent turkey killing patterns at 40+ yards is your 870, the 3" Winchester HV (Black Shell) with 1.75 oz. of #6 lead shot through the Strut-Stopper Xtreme (SSX) Turkey Choke. Those shells can be found almost everywhere, are inexpensive, about $10.00 - $12.00 per box, proven, and have accounted for more turkeys than I can imagine over the last 10 years. The SSX is a proven, premium quality turkey choke, approved for all turkey loads, including all tungsten-based shotshells, yields excellent patterns and is priced very economically under $40.00.
Your 870 may have come with the R-3 or the new SuperCell recoil pad. Either way, I'd suggest that you use the Shooter's Friend Recoil pad over the factory pad. It's made of a very soft material that has a much larger "footprint" than the factory pad. It distributes the recoil over a larger area and the material helps to absorb it and reduce felt recoil by 70%. I've used these pads on my guns for years and really recommend them. Again, they are very inexpensive and you can transfer the pad from one gun to another.
I would be very confident taking the above combination to the turkey woods anywhere.
Lastly, whatever "combination of ingredients" that you choose, I'd recommend that you spend some time at the patterning board, get to know your gun and most importantly...have fun!
P.S. If I can help in any way, just let me know and I'll be of all possible assistance.
"If he's out of range, it just means that he has another day and so do you."