My own taste runs toward something like the Cannondale T2000 ($1,400). It's a true touring bike, with lots of braze-ons (the fittings on frames that are used for attachments) for installing racks and fenders, room for big tires, and a relaxed frame for a comfortable ride. The advantages of such a design are more hand positions on the handlebars, better aerodynamics, and a more forgiving road ride. Its sibling, the T800, has a similar frame, a lower-priced component set, and sells for about $900. Trek's 520 is another good touring bike, similar in many ways to the Cannondales but for the fact its frame is steel. The upside is a slightly smoother ride; the downside is it could corrode over time if subjected to frequent wet rides. The 520 is priced at around $1,000.
Depending on your size, you can probably buy one of these bikes secondhand. Doing so would save you hundreds of dollars, allowing you to get the bike you really want and need, while still making your budget.