For tax purposes, it does not matter which state you reside in , once you have a green card you are a resident. For immigration status you are a permanent resident.
For state residency, it is the state you call home, where you return to after short absences and where you have most connections. From your post you appear to be a resident of Virginia -- home, car etc. However, for military persons ( and their family ) generally it is the Home of Record that rules -- most of the time.
Does that help ? or muddle more ?