An oral temperature reading is more accurate than an armpit reading by about .5 degrees celsius. An oral reading not quite as accurate as a rectal reading, but the difference between an oral temperature and a rectal temperature is usually around .2 degrees celsius. So that may be accurate enough for your purposes. A good ear thermometer can also give an accurate reading--they're better than they used to be.
A fever is generally considered about 38 C measured rectally, 37.8 C measured orally, and 37.2 C measured from the armpit. A low grade fever is generally considered between 37-38, although some people just naturally have a regular temperature in that range.