My .02 - do a 4 or 5 day trip first as a warm up and carry all the stuff you plan to bring on the week long trip as practice. It probably isn't that much more, just food, but it might just open your eyes to what you do and don't need and make the whole thing a lot easier. Maybe bring a friend and just offer to carry all of the food and you'd basically have your real pack.
As for a topo, the Trails Illustrated High Uintas map is a good overview but not a great detailed map. For detailed, you have to either get a LOT of USGS 7.5 quads or do a custom job. I printed up a set of 11x17's with Trimble's MyTopo service when I was planning my trip. The MyTopo service sucks but if you have a lot of time on your hands, it can produce good maps and it doesn't cost much. Being able to print larger than your home printer will be very handy. Might be worth saving them as 11x17 PDFs and then taking a trip to Kinkos or something. Is it still called Kinkos?
As for the trail itself, I didn't end up doing it all due to illness, but I've still hiked a large portion of it and a lot of the rest. You'll be above tree line a lot and the trails aren't very great up there. Be prepared and capable to navigate accordingly. The sheep also do a lot of damage making picking the right trail more difficult. Signage is not to be relied on. There is still a man missing up there from two years ago that was attempting the route.
If you plan to fish, you might want to reconsider. Unless you have a lot of time and energy on your hands, there really aren't that many fishing opportunities along the main route. It wouldn't hurt to pack something like a Tenkara rod setup which would only cost you ~5oz but packing an actual rod with gear is likely not worth it.
If you search the interwebs, you'll find all sorts of crazy stories. Inexperienced folks heading out there with 60+ pounds on their backs. Cans of red bull, bear canister and all sorts of ridiculous things you would never need up there. Really think about what you need to carry and you'll enjoy yourself so much more. Build your way up to it even. There are tons of 4-5 day trips that will bring you as much or more satisfaction than the Highline. Sure, it's awesome to have done the whole thing, but if that is what matters you're just hiking for ego and not enjoyment and what's the fun in that? And don't overlook the first part coming out of Leidy - it's highly underrated. Take your time.