There are contractors who make seamless gutter on site to the exact diminsions of your house. I just had a crew over to do my house for $385. I can hardly even buy the material for that price. I know, to look at gutter at Lowes or Home Depot you wouldn't think it would cost so much. But then, start counting up the little accessories you will have to have to install it and, if you have to splice it, I gurantee it will drip forever.
You may want to get more than one bid on this just to keep them honest.
Your roofing contractor will put an exclusion in his contract concerning rotten or loose deck that may be found under the old shingles. Your loose drip-edge indicates you have some bad decking. They should include new drip edge in your contract and it should be the larger, galvanized kind which will not bend under a ladder.