Learning path for the proof of the Weil Conjectures

I'm not an expert, but here is how I would plan my trip:

There are obviously two parts: rationality + functional equation + comparison with Betti numbers (which follow from the construction of etale cohomology) and the Riemann hypothesis (which is much deeper).

I would therefore follow the following plan:

1. Learn classical algebraic topology, esp. singular cohomology, Poincare duality, Lefschetz fixed point formula, Leray-Serre spectral sequence.
2. Learn an overview of $\ell$-adic cohomology, without technical details. First, understand how a good cohomology theory like in 1. above will prove the first part of the conjectures. Then understand etale topology and definition of $\ell$-adic cohomology groups and how the Frobenius morphism happens to act on them.
3. Technical machinery underlying $\ell$-adic cohomology. I haven't studied this myself very well, but Milne's book seems to be a standard reference.
4. Read Deligne's Weil I article. It's beautifully written and you don't need much more than 1. and 2. above. The main technical tool is the use of Lefschetz pencils, which is there just to make induction on dimension possible. You can just assume Lefschetz pencils exist, or look to SGA if interested. Note that in Deligne's approach it is crucial to work with constructible sheaves, not just the constant sheaf.
5. Read Deligne's Weil II article. It reproves Weil I and adds much more, but is much longer and more difficult.

Note: 3. and 4. above might be mostly independent. A very good reference is Katz's article "L-functions and monodromy: four lectures on Weil II".

Dear Javier,

I wasn't sure what to make of your question at first, but I think I understand some of your motivations from your other question. If you have interest in this area, then I think it would be useful to study etale cohomology. Regardless of whether or not you get to the Weil conjectures, the etale topology has all kinds of uses, so the effort would not be wasted. Aside from the references that you mention, see the answers and comments here Textbook for Etale Cohomology

Here are Uwe Jannsen's lecture notes on étale cohomology http://www.mathematik.uni-regensburg.de/Jannsen/Etale-gesamt-eng.pdf and Weil I http://www.mathematik.uni-regensburg.de/Jannsen/home/Weil-gesamt-eng.pdf and Laumon's Fourier transform http://www.mathematik.uni-regensburg.de/Jannsen/home/Garben-gesamt-engproof.pdf.

For Weil II, there is also Kiehl-Weissauer.