The following seems very relevant to the OP from a *historical* point of view: a pre-[Tohoku](https://ncatlab.org/nlab/show/Tohoku) roadmap to algebraic topology, presenting itself as a "How to" for "most people", written by someone who [thought deeply about classical mathematics as a whole](https://www.jstor.org/stable/2320582?seq=1#page_scan_tab_contents). The source is 

> [Ernst Snapper](http://www.ams.org/notices/201301/rnoti-p86.pdf):  *Equivalence relations in algebraic geometry*. Bulletin of the American Mathematical Society,
Volume 60, Number 1 (1954), 1-19.

However, I feel it is necessary to precede the reproduction I give below of this 'roadmap' with a *modern*, cautionary remark, taken literally from http://math.stanford.edu/~conrad/:

[![enter image description here][1]][1]

That said:

**A 'roadmap' from the 1950s.**

[![enter image description here][2]][2]

[![enter image description here][3]][3]

It is interesting, and indicative of how much knowledge is required in algebraic geometry, that Snapper recommends Weil's 'Foundations' at the *end* of this "How to get started"-section. 

  [1]: https://i.sstatic.net/oZ8kB.png
  [2]: https://i.sstatic.net/4EIhn.png
  [3]: https://i.sstatic.net/hlQkw.png