With a roof mounted solar panel, unless you are within the tropic of cancer and the tropic of Capricorn (within 23.4 degrees of the equator) on the right day, you won't get 200W. At the 45th parallel, you need to tilt your solar panel to 30 deg above the horizon at the summer solstice and to 60 deg above the horizon at the winter solstice to get full sun on the panel. Take your latitude and subtract 15 deg for summer and add 15 deg for winter for direct sun.
But if you have full sun, or at least a decent amount, your solar panel will output at around 20 volts, which means a max of 10 A. If you have very little sun, the panel will output around 13 V - but only an amp or two.
14 gauge wire is just fine for your 200 W panel.