I would definitely do either oral or vaginally. I've read that vaginally is the most accurate between the two though. With oral, temps can be lower if you sleep with your mouth open. However, it seems that most still do oral regardless unless it's giving too inaccurate of results in which they may decide to temp vaginally to see if the if it's from sleeping with their mouth open or if there's something more going on hormonally.
Some prefer to just start with vaginal temping, but most find oral easier. So maybe start with oral temping and if you find your charts a little erratic even though you're being consistent with temp times and sleep pattern switch to vaginal.