This tree is in the open getting good light already, so watch out on how much is cut. I would start at the base and work my way up. Take out that dead wood and small stunted stuff under the main canopy. It's not going to do anything anyways as far as fruiting, it's just extra wood. Then go up as the others have said and take a couple uprights. Pick ones that are gnarly and have a several other uprights (not the big 4-5 leaders) and lower branches off of them. This way you essentially are only making one or two cuts to the tree and there will be less suckering. Although you may have to make a few more cuts just to get them out. Make those cuts on the wood you are taking out..............................Again not much though, just 2-4 spaced evenly around the tree! If you take out a bunch, making a ton of cuts, it will just sucker like crazy!!!!! I can't stress this enough.
Take your time, this will be about a 3-4 year process to get it in decent shape. I wouldn't try to get it down to one leader, it's too far gone for that. Another good thing you can do is prune off any suckers that shoot up from the cuts you have made in mid summer.