The most convenient shifters for a dropbar bike are "brifters" (combined brake levers and shifters) that Shimano calls STI and Campy calls Ergo. The downside is that they are by far the most expensive and are all indexed so you woiuld need a bunch of other expensive components to go with them.

Next for convenience are barend shifters which are much less expensive and, since most offer a friction setting, can be used with nearly any set of components.