Drive; there really isn't a viable alternative. The presence of the petroleum industry in this corner of the state has the advantage for the driver of providing a somewhat higher density of towns with gas stations, etc., than in some other parts of New Mexico. The northwestern reaches of the region, however, are still very thinly populated, and if you're driving in this area e.g. between I-40 and Roswell, keep an eye on the gas gauge.
US and state highways in the region are generally in good shape. However, if you're heading into the mountains, particularly the Guadalupes, for outdoor adventure, check locally on the condition of Forest Service roads, which can be very rough; some will challenge even the experienced 4-wheel driver.