I believe Hartshorne and Vakil's notes are two most popular text currently, so my question is about how to choose the text.
I have worked through the first 4 chapters of Vakil's notes and now I am thinking whether should I continue or try to study Hartshorne.
Vakil's notes are very well-organized. Especially, the exercises appear just in the right time, and there are more explanation of the exercises, so that I know what I am doing. But the problem is most arguments are given in the form of exercises, which means I am always stuck. The typical situation is after 2 hours work, maybe I am still in the same page. But the book has almost 800 pages! Hartshorne has some proof, the exercises also have some explanation. So maybe I should try to work Hartshorne?
Another question is about exercises. How long should I spend for an exercise that stick me. Should I look up a solution after maybe struggling for half hour? There are solutions for Hartshorne, so maybe study Hartshorne is more convenient since it is easier to look up solution?
Also, what is the right pace to learn the stuff? I mean should I worry if every day I spend 3 hours to learn the stuff but I only finish 1 page?( I know maybe I should spend more time, but unfortunately I am teaching myself algebraic geometry and I have other classes currently)
I appreciate any advice, thanks!