You may want to check out this post. It's from /r/totalwar, but it excellent and well sourced, and covers the difference between the various type of Ptolemaic troops. He includes a lot of illustrations so you can get a good feel what they might have looked like.

Basically the Ptolemaic army had a core of professional mercenaries made up of Macedonians and other hellenized peoples. They then had the kleruchoi, which formed a militia reserves. The kleruchoi received land in exchange for being available for service in times of need. So farmers most of the time, but soldiers when need be. These tended to fight in Greek style phalanxes and largely consisted of Greeks living in Egypt, or Egyptians of certain rank, but who also would have been equipped and fought in a Greek fashion. There was also a fully native force called the machimoi. Early Ptolemies didn't raise or use the machimoi. But as the Romans conquered the world, recruiting mercenaries became difficult.

But kleruchoi and machimoi probably wouldn't have been pulling door watch duty anywhere except in times of war, and never at the palace. So what you'd usually see is a mercenary soldier. The core of these would generally be trained in phalanx fighting and would be Greek or at least hellenized. But the army would also include Celts, Nubians, Italians, Nubians and more. And these tended to act as auxiliaries to the phalanxes. They would be equipped in their traditional gear and would be expected to fight after their traditional fashion.

The Ptolemies did have a Royal Guard (Basilikon Agema) which was basically their elite phalanx unit, 3,000 men strong. They were recruited from across the hellenized world and would have included men from the kleruchoi. They handled security at the palace in Alexandria.

So what would a guard look like? Generally they'd be Greek, or at least hellenized men from the western Mediterranean. Egyptians would be relatively rare but were a possibility. They would be dressed and equipped in a Greek fashion.