Your list seems like overkill to me.
As far as geometry, Kiselev is basically a rehash of Euclid, so I don't see the point in studying both. Just pick one. I don't think you need the solid geometry parts of either.
If using Euclid: -- Euclid contains stuff like number theory done in an ancient style that is now only of historical interest, so if using Euclid, skip that. Euclid's definitions of terms like "line" and "point" are nonsense by modern standards, so skip them as well. (The Russell book will give you a better modern mathematician's intro to how definitions work.) Make sure to work from a well-annotated edition of Euclid. IIRC there's a very good free one online by Kirkpatrick. Some of Euclid's arguments have flaws (including his very first theorem).
The Russell book spends a lot of time developing what we would now call set theory, but it predates the standard modern formulation of ZFC, so I'm not sure I'd recommend using it as an intro to that topic. I don't think any significant amount of the material from this book is needed for Spivak.
I'd avoid making an affectation out of reading books by famous people dating to 100-130 years ago.
For algebra, trig, and geometry, you can get all the preparation you need from any crappy high school books you can find at the library or half.com. The hard part about Spivak is going to be the that it's written for an audience of future mathematicians, so it doesn't dumb things down, and the problems are reputedly hard.