I have thought that it would be a great idea if people would have the Avi Ezri of Rav Shach and learn it every day. The reason I say this is that there is a depth in Torah that is hard to reach on one's own efforts. Now this kind of depth certainly is there just in the Oral Law [Gemara]. However it can be hard to reach without Rav Shach. [Certainly this kind of depth in the Gemara and Rishonim also can be seen in Rav Haim [Soloveitchik] of Brisk and his other disciples. But Rav Shach brings that kind of learning to it peak.]  

I might add here that if you go into any Litvak yeshiva, they always talk about the importance of the Rishonim and they are right about that on one hand. But on the other hand they are not mentioning that then after the morning learning session they go and hear a class from one of the teachers. And that class always contains  the achronim, e.g. the Ketzot HaHoshen, R. Akiva Eigger, the Pnei Yehoshua, Rav Haim of Brisk, and his disciples. They are not actually thinking that you on your own can just open up the rishonim and understand their depth.

So I see the learning of the achronim just as important as the rishonim. But that already depends on one's level. At first probably the best is to go to the Maharsha and Pnei Yehoshua. Then after doing a few tractates like that, then to go to to Rav Shach's Avi Ezri.