Okay, I have some recommendations for you on the assumption that you are going to be changing your roof.
First regarding the eaves, when you take up the shingles to replace your roof, cut the rotted decking up from the eaves however far is necessary, and replace it with new plywood. When you go to replace the roof, make sure you put drip edge along the eave of your roof, and since you had water problems there, check you facia trim to make sure that the drip edge is covering OVER it. If it isn't then get wider drip edge or redo your facia trim to make it come up high enough to be covered.
Regarding ventilation, like you said, the house is divided into two sections and adequate ventilation can be difficult to get. I would suggest a power vent hooked onto a timer, but that would require some wiring. Another option is to put turbine vents strategically placed. They install easily and do a good job sucking air out. Ridge could be an option but I wouldn't recommend it.
Regarding the cheapest roof, it would probably be your standard 3tab shingles. Or check around and you might be able to locate some dimensional shingles on sale. Or a lot of metal suppliers run specials on their metal so check them out too.
On the felt, you wouldn't need to put Ice&Water shield on the whole thing, altho putting it around the perimeter of the roof isn't a bad idea. I would highly recommend the Grip-Rite shingle layment for underlayment. Really awesome stuff. It comes in 10square rolls. Check around and you should be able to find it at more/less $115 a roll.
Since you have a cathedral ceiling it will be hard to get insulation in there altho it is possible with blow in stuff. If you don’t mind metal roofs, getting a good insulated roof would be a lot easier. The way to go about that is to put Double Bubble wrap foil insulation down directly on the decking. Then put 1x4 or 2x4 lathing on top, every foot center. That will give you a good insulation and also put an air space between the foil and metal. I hope that helps!!http://www.roofing.com/forum/posting.php?mode=reply&f=2&sid=500309f5232f5257c35e9b04e1c5d9d0&t=13034#