A 10A controller is enough for 150 watts, maybe 200 watts of solar.
About 2 years ago I bought a 75W panel and a Morningstar SG-4 controller from solarblvd.com for about $125 total. I rigged the setup to plug into the trailer's 12v pigtail (that goes to the tug) and left the panel unmounted. My controller is outside, too, but it is made for that.
For storage off site, a mounted panel and indoor-mount controller probably makes more sense to deter theft. Shop around a bit, you can get far more solar than that 15W and it will be money well spent. It will help you on those trips when you find a great place to spend a day or two but there's no shore power.
