Brifters offer the benefit of convenience with the main tradeoff being complexity and cost. When they work, they're brilliant. When they don't, you're stuck with the cost and inconvenience of replacement or repair (in the case of Campagnolo).
The cyclocross suggestion might be hinting at the traditional use of (simpler and more reliable) bar-end shifters, though many cx-ers employ brifters these days.

If you don't have any significant hills, SS is a great way to go, or perhaps a 3-speed IGH.