So, first off, I just want to repeat that this is how I personally run things, so it isn't a RAW interpretation of anything, just how I personally handle spirits for magicians for my games.
That being said, I will add that the restriction on defining powers applies primarily to the Elemental Attack and Engulf powers. Those powers (and any others that end up like them) have different effects based on an "element" but the listing in the powers a spirit gets doesn't say "choose one." So, for example, It doesn't affect the powers that explicitly can be different each time you summon a spirit (like Optional powers: Innate Spell, Skills, or Improved Sense), those specifically state that you have options, and those options can be different each time.
I also want to add that it doesn't limit what Optional Powers you can take, or the order that you take them. The optional powers do add a bit of variety each time, it just adds a theme that those optional powers might manifest as.
Now, I did say that the choice was a thematic one, so any of these limitations would be based on the theme chosen and can still vary as appropriate within that theme. A Norse tradition mage could specify that all Guardian spirits look like Valkyries, so it only makes sense that the Natural Weapon power would manifest as an actual weapon. That weapon might normally be a spear of some sort, but it could just as easily be a sword, or an axe, but claws wouldn't be fitting in this instance. I don't remember if Guardian spirits get elemental attack, but going on that theme, they would probably wield lightning (electricity) if anything...
Most magicians don't summon "monkey spirits" they summon spirits of beasts. For most magicians I would probably ask the same sort of thing for their beast spirits, "what sort of beast does your spirit manifest as?" For many, it wouldn't change much, and depending on tradition their might be a limited list of creatures that make sense. My shinto mage, for example summoned foxes as her beast spirit, because in shinto, kitsune are trickster spirits. Shamans that have chosen an animal totem, likewise, probably summon beast spirits that are aspects of their totem. There might be some variation for a magician that doesn't follow a specific totem, but I think for a lot of people when you ask them for a combat animal, their mind is going to go for something first, and that's probably what your combat spirit looks like.