I am a high school student who has finished the standard hs math curriculum. After working through an intro to proofs, logic and set theory (Velleman's How to Prove It), I am looking to study some proper pure maths. My motivations are to have fun, and to prepare myself for accelerated college classes such as Harvard's Math 55 and UChicago' Honors Analysis. I am considering learning either analysis or algebra.
If I pursue analysis, I will most likely use a combination of baby Rudin and Apostol, although I am open to suggestions (Tao and Abott?). If I learn algebra, I will use Artin, supplemented by Benedict Gross's youtube lectures.
I have not been greatly exposed to either field, but from the little I have read in the Princeton Companion of Mathematics, algebra seems more interesting. Is it more important to study what fascinates me more or what fits into my education better?
Any advice is appreciated.