>>11492788Either or is fine, and D&Fs length is mostly due to the amount of examples and exercises, if you take those out it isn't nearly as long. Again, look around and see which you find most appealing. As for topology, while munkres is fine I do think there are better options, for example, lee's topological manifolds book is quite nice, though I suppose munkres is a bit more leisurely, I prefer the former. It really only requires maybe the first four chapters of rudin as background and a little algebra, but all of this is covered in the appendix. It'll cover some of the material is fomenko as well, though I'm not sure you'll really need most of fomenko for what you want to do, so you might want to drop that one (though it is a good book, though worth mentioning a lot of books develop spectral sequences over again so it might be okay not to focus on it here).
As for differential geometry, your choices are a touch confusing. General theory of smooth manifolds, Tu is great as an intro, lee is also fantastic for basically presenting everything step by step with tons of examples. I would also say the latter is great at presenting not only the theorems, but the kinds of techniques you would typically use to attack those kinds of results, really learning you ABC's (when confronting embedded manifolds, Always Be using slice Charts). Though de Carmo is also great for your purposes, I would definitely supplement one with the other.
As for AG, the nice thing about CAG is that you can sort of skip over learning regular AG and just sort of dive in. Certainly, Harris or Voisin or Demailly don't assume you know what a sheaf is. Also, Miranda's book on algebraic curves builds things Riemann surfaces and fleshes out some really beautiful mathematics.
Finally, when it comes to actual study habits, again, consistency is the key. Furthermore, make sure to carefully work through every result, don't just read the statement of the theorem and move on, try proving it yourself.
