I'm playing a magical boy or better version of Tuxedo Mask. I want to emulate what D&D 3.5e Familiars can do. Would a Power or an Advantage be better to do so? Minion, Summon, or Sidekick? How do I emulate the ability for my Familiar to be able to cast the spells I can as long as they are within 60 feet from me?
I would suggest either Sidekick or Minion if your Familiar is always with you. Sidekick is best if you want to avoid them dying quickly as per the top-ranked answer at Why is there a large difference in CP between the Advantages Minion and Sidekick? although it will make them more expensive.
To let them use your powers, you basically have them buy those powers, with a Limited Flaw that they can only use them when within 60 feet of you (your GM might decide this is more of a Quirk if this will prevent it less than half the time). This will let them use that power as their action.
Alternately, that could be a good case for the Indirect Flat Extra. Three ranks should nicely handle "From nearly any point, any direction your Familiar is facing" (Honestly, it's sort of an Indirect 4 (any point, any direction) with a Quirk of "Originates from my familiar"). This has the drawback that it's your action to fire off the power.