Welcome, you've chosen one of the best floor plans that Winnebago's produced. I have a 2002 Suncruiser 35U so feel free to send me a private message (PM) if there's anything I can do to help.
Also, it's a good idea to set up a signature (via the User CP) similar to mine that lists the year and model of your MH. That way we'll know what you have and you won't have to enter it every time you post.
Your number one priority will be to take care of any leaks (or potential leaks) along with making sure the roof edges are properly sealed to the aluminum extrusion. Here's a helpful video, hopefully your's isn't this bad:
Another common area for leaks is the windshield. You can research windshield leaks here on Winnieowners:
I solved my windshield link with a strip of Eternabond tape across the top edge of the rubber moulding at the top of the windshield. Gorilla tape will also work as a temporary fix.
You can access a lot of info on Winnebago's site via the "sticky" posts here:
And this is a good resource. Even though it's based on a 2002 Journey, the issues and solutions will be the same for your 35U:
(roof repairs are covered under "Chassis Repairs and Fixes)