Oil change + replace battery, which comes first ?

If you have any reason to suspect the quality of the oil (i.e. signs of water/foamed oil on the dipstick, etc), I'd do 2 oil changes, drain and refill while cold, start let the engine warm to operating temperature, then do another change. But if the oil seems fine, then just do whatever your normally do when you change it and change the battery whenever you want.