I'm personally not a big fan of lava rock in most situations - it kind of looks out of place. Other types of rock tend to look more natural.

I'm not an expert, but based on my DIY knowledge mulch is no worse than rock against your foundation, as water actually seeps through rock faster than mulch. The problems arise when you have plants or grass that require watering too close to foundation. The most important thing to ensure is that the ground UNDER the rocks or mulch is compacted & sloped away from the house to keep water from pooling against foundation. Any homebuilder or civil engineer should be able to tell you recommended slope for your area/soils, but genrally +/- 1 foot of slope in first 10 feet away from house is sufficient.