Just don't underestimate your factory tubes. Before buying aftermarkets, one of your IC/M/IM chokes will probably give you good results. It's fairly standard to shoot a 4x4' piece of paper and draw a 30" circle around the densest portion of the pattern and then determine your pattern percentages and also consider the even-ness of the pattern.
You will have to choose your shells for the game and ranges you're experiencing. F shot may fatally penetrate a goose further than BBs, but at those extended ranges the pattern density also goes down and you would just be playing luck trying to get one of your 50 pellets to hit. For all of my duck hunting, cheap 2 3/4 or 3" 3s can handle it all. I'm usually not shooting further than 30 some yards, so I still have plenty of juice to put down a duck while also having enough pellets to make it easier to get a good dose on the duck.
For geese, I usually hunt at longer ranges. Big geese are usually harder to take down than a mallard, so that there means I want a larger pellet, plus the fact the ranges are further (you can relate this to rifles in that the larger the pellet, the greater the mass, sectional density, and ballistic coefficient so the lower the velocity loss and therefore the further you shoot the greater and greater the energy advantage). Larger pellets mean fewer, so I take advantage of running 3.5" shells to put more of the odds in my favor. In my case it's worth the small cost increase to run them. I usually opt BB or BBB, and I'm willing to sacrifice some velocity for payload. Again this is to suit my hunting. If I'm decoying to 20 or 30yds I'd be all over 3" 2s. One shell that has my interest is the Hevi-Metal. Using these increases your pellet count 20%, but the drawback is about a buck a shot (and I just ordered a case of 3.5" bbs for $140 shipped). Same cost as Black Cloud, which, after using, doesn't seem to be worth the cost increase. Maybe hevi-metal would be worth the dough.
I don't really care for hevi-shot, remington hd, or other 12g/cc density shot. In fact I wouldn't use any expensive steel or high density shot unless 40yds was a close shot. The performance vs cost just isn't there. They're a high density nontox shot, meaning you can use smaller shot to get the same penetration as larger steel shot at a distance. Although the pellet count is increased by using the smaller shot, the difference is not that stellar and the cost does not justify it IMO. If I was to pay the price for a high-density shot, it would be Federal Heavyweight (15g/cc). You can use way smaller shot and get way higher pellet counts and still get the penetration of the largest steel shot, which really puts the odds in your favor. Once again, cost is a factor, running over $4 a shot regular price but it can be bought for $1.60-$1.80/shot.
Just some things to consider. In a nutshell, smaller shot and less of it for closer range and smaller birds, larger shot and more of it for larger birds and longer ranges. High density is a waste of money excepting long range shooting with federal heavyweight 6s.