I'm guessing from your weight that you might not be very fit? In your specific case I think your goal might be to make you as comfortable as possible on the bike with respect to the contact points (seat, handlebar, and overall position) and to match the gearing to your weight and fitness level. I have my doubts that a standard off-the-rack bike will meet your needs.
I have something completely different to suggest: a fully customized steel-framed Jamis Coda or Jamis Coda Sport (the Sport has a carbon fork). This is classified as a street bike, but the specs below will turn in into a fabulous touring/do-everything bike.
SPECS:
--Full mountain gears to get you up the steepest hills: 22-32-44 front; 11-34 rear.
--Nitto North Road handlebar for a more upright position:
http://www.benscycle.net/index.php?main_page=product_info&products_id=6397¤cy=USD. For climbing hills you simply move your hands forward.
--A wide but not ridiculously soft seat: Selle Royal Ellipse Moderate Women's.
http://www.nashbar.com/bikes/Product_10053_10052_507970_-1_201632_10000_202448--SRAM X-5 twist grip shifters: Very comfortable and simple to use. Get the X-5 rear derailleur too.
--Soft ergonomic grips. This shape:
http://www.meritline.com/ergonomic-double-density-bicycle-handlebar-grips---p-59594.aspx?source=fghdac. Get the thickest gel gloves you can find and make sure the gel is in the palm, not just the heel of your hand.
--Rims: Definitely agree with 36H
--Tires: Vittoria Randonneur Pro 700 x 35
I have this exact bike (except my tires are 700x32). For me personally, this is as close as you can get to heaven on wheels. If you find the right shop the modifications aren't prohibitively expensive. The Coda should come in at under $700 fully modified, from a base price of $500. The Coda Sport will be about $850 modified.
I know my suggestion is not something you were thinking of doing, but consider that thousands of Europeans tour on bikes very much like the above---not on dropped bars. And there are many bike tourists in the U.S. who favor this set-up.
I have biked up to 2000 miles a year on a hybrid with an upright, swept-back handlebar. Don't be worried about multiple hand positions with this bike. I find that when the bike is set up right and I have thick gel gloves, I don't need more than one or two hand positions. As a former carpal tunnel sufferer I can tell you that this upright bar is great for your wrists.