Gee, $3,000 will cover most bikes, even a lot of custom bikes.
I was in the same place as you are about a year ago. (how time flies)
I decided I didn't want to spend gobs of $$ until i knew whether or not
I was going to do roadbiking. so i bought a $700 bianchi veloce on Ebay..
and I am learning everything backwards. Like I finally know what size I am,
after bike shop people have looked at me on the Bianchi and said "you look comfortable" I know I like riding road bikes, but it's a chore to find a bike that fits. You say you are big, do you mean tall? Because that will really help in finding a new bike.
So, what I think you ought to do is beg or borrow a road bike, any road bike and see if you like it. And then if you do, start researching (like where Knot told you to go) and go buy that $3000 bike! and weight DOES make a diff, for $3k you can buy a darn good bike!
Just curious, what bike tour are you doing in Italy?