I've killed 2 with my Mossberg 935. Can't recall what choke I have in it. Have a little more than $300 in that gun though. My 835 sits in the safe as a backup since I got the 935. I think I paid about 2 bills for the 835.
I'd definitely make sure you get a 3 1/2" gun. I dropped my last one in 2008 from about 50 yards. Like that power of the 3 1/2.
You can get a new single shot for less. I've been using an H&R single shot 10 gauge for a while and it drops em. Got a red dot also, which helps. They come with one bead on the barrel and it's hard to get lined up on target. I paid 2 bills for it, but I think they might have gone up in price.
mossberg 835 with an undertaker choke tube, shooting 3.5" copper plated #5 shot. mine patterns better than any gun Ive ever had with this combo. inexpensive to boot.
There were several in the forums here. Are you going to shoot 3 or 3 1/2" shells? The single shot H&R 12 gauge turkey guns are new for around 200. That may be a good place to start.
Loved my 870 supermag. Had a Jelly Head tube on it and it was really tight patterning. They can be picked up for around $300 for the all black sportsman model.
I shot my 10ga 5 times when sighting in my red dot. It left a bruise. I think you can get a little more distance out of a 10 and usually you only get one shot at a tom anyways, so it doesn't bother me much. I also am 6' 200lbs".
I have a Rem 870 supermag express with a good tube and i wouldn't hesitate to take a 55 yd shot go for the 3 1/2 if you think its to much you can still shot 3. I like to chase turkey with my mathews now.