My bike was breaking tons of spokes with the stock wheel. After about 20 breaks, I rebuilt it with a good rim (double-walled, about $25, an Alex Adventurer) and DT butted spokes.
My spokes were all breaking at the elbow, which I guess is indicative of load/unload repetitive stress from pedalling, NOT from load.
When I built it, a friend advised me on how tight to make it; his advice was "Crank the nipples on the drive side down until you think you're about to strip something, while keeping the dish and true correct." What you DON'T want to happen is for the spokes to be loose enough that the trailing spokes can unload when you're powering up a hill or something, because unloading then loading up again causes them to crack eventually. You want enough tension on the spokes that even when you're pushing as hard as you can up as big a hill with a full load that you ever get, the trailing spokes still have some tension on them.

FYI, the factory wheel broke its first spoke at about 500 miles, I gave up around 1500 miles, the replacement I built now has over 13000 miles on it and I never touched it after finishing it, and it's still dead true and no broken spokes.