Two trunks suggest that the tree may be a seedling so the fruit may be about worthless. If you choose to prune it anyway, the easiest way to manage it is to prune it to a weep if the tree is conducive to it. Prune out upright growth in favor of the weaker weeping wood.

Where branches rub remove one branch choosing on the basis of economy of wood. That is you aim to harvest the most light with the least structural wood as possible. The amount of smaller wood on large branches should be in ratio to that branches relative size. In other words a six inch diameter branch should have access to twice as much light as a 3 inch.

I'd have to write about ten pages to spell the whole deal out.

Harvestman, I have a high speed connection, so downloading 10 pages will be no problem. A comprehensive pruning guide that we can all just refer back to every time a pruning question is asked will really be helpful. (-;

Brandon, my computer recently crashed and my word files are locked up. I've written a great deal about pruning fruit trees and renovating old apples and I will be pulling those files out soon. Send me an e-mail to alandhaigh@gmail.com and I'll send you some of what I have in a few days.

I would prune the tree in summer and just take out some of the upright growth.
Summer pruning really slows apple trees down.
If you get into heavy pruning in the winter the tree will respond by sending up lots of fast growing shoots.
Your tree sounds like it has plenty of vigor, you will tire of pruning before it tires of growing.
Then next year you could thin some other branches if its really overgrown.
I think the best backyard trees are ones that are covered in fruiting spurs, and fruit and have run out of energy to produce too much wood.

Actually, you can get more done and the same deinvigoration by pruning in the winter and mopping out the suckers in the mid summer- why waste time. I manage a lot of apple trees by summer pruning only because I can't get everyone done in the winter. It works just as Mike says, but one tree shouldn't get you very tired if you have the right tools. I recommend a Silky Gomtarro 300mm large toothe for sawing and a good chain saw for anything over about 5" diameter. The Bahco orchard lopper is the best I've found (and I've tried most) and either a top or the line ARS or a Felco hand shear. When I use a Felco I use the 13. Of course if you only have one tree to prune you may not want to spend all the money for the best tools, but at least get the Silky saw. All of these are available from AM Leonard.

I work on an old transparent apple tree in WA (south of Spokane) when I visit in Dec and summer. In Dec I cut off vertical branches around 7-10 feet and let lateral growth extend. I thin lateral growth to let light in during both periods. Apple trees in this area have vigorous growth and though this tree looks pretty bleak after I do Dec pruning it produces a fine crop and its easy to pick.