I studied Analytic Number Theory by Apostol (Introductory and Advanced vols) and I learnt very good! And because of that studying of the first two chapters of Montgomery's book was possible but it is very hard or sometimes impossible to study from chapter 3 onward. I chose the mentioned Montgomery's book because of amazon reviews but I stuck in it!
Is there any intermediate book between those Apostol and Montgomery? or any advice for better reading not-simple-written Montgomery's book?
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You can study the wonderful book Opera de Cribro by John Friedlander and Henryk Iwaniec. The book has got excellent reviews and the authors are the leading experts in Sieve methods!
On a lighter note: Here is an exposition on Number field sieve written by C. Pomerance.
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Here are some course notes on Sieve methods from a master's course given by Prof. Lola Thompson in Leiden University. I hope this helps!
I don't think there's a simple book on sieve methods – sieve methods just aren't simple – but Cojocaru and Murty, An Introduction to Sieve Mehods and their Applications, is worth a look. It's in the London Math Society's Student Texts series, which is encouraging. The preface recommends Chapters 1 through 5, and 7, for a senior level undergraduate course, says Chapters 6, 8, and 9 are at the graduate level, and Chapters 10 and 11 are at the seminar level.
There's a 20-page chapter on sieves in Bateman and Diamond, Analytic Number Theory, and 25 pages in De Koninck and Luca, Analytic Number Theory.