Minzi, here in Northern California, we probably have a least a dozen different varieties of Eucalyptus, all introduced. When you say you have "red" gum on your place, is that the same as "red-flowering" gum (i.e., Eucalyptus ficifolia)? If so, that is one of the most showy gums we have here. The flowers are spectacular. Anyway, I will check to see which are the gums that are most common here.
In fact, back in the early 1900s, California embarked on an ill-conceived project to widely plant Eucalyptus for lumber production. It didn't take them long to figure out that the wood tends to be too brittle for most lumber uses and that each Eucalyptus grove they planted was an inferno waiting to happen.
These days, folks plant groves of gum as wind breaks, and individual specimens in decorative landscapes. Fast growth, drought resistance, beautiful silvery foliage and, sometimes, showy flowers, make them a great choice as an individual ornamental tree.