Hi Becke,
Yes, the Falco mysteries by Lindsey Davis are best read in order, at least the first 3 or 4. Then it's easier to be out of sequence.
It's interesting to me that Davis had ended the Falco series and started a new series featuring Falco's adopted daughter Flavia Alba. Having seen ancient Rome through Falco's eyes, it's a whole new ballgame with a young woman in the narrator's seat. Davis delves much more deeply into the domestic lives of Roman women, servants and slaves than she did in the Falco books. A very interesting broadening of perspective.