This is truly a classic paper. Read it to appreciate Bush's great vision which has NOT yet completely realized.
If possible, read everything starting from section 6.
This is a very good overview paper of IR, though it's a bit out of date and slightly biased toward empirically effective techniques. Your goal of reading it is to know about the general history of IR and a summary of IR techniques from empirical perspective. Read the whole paper.
Read the entire chapter 6.
Optional. Read whatever you feel is useful to you.
Read 8.3 and 8.4. Other sections should also be very interesting to read, though not required.
Read entire Chapter 1 and Sections 3.1 to 3.4 in Chapter 3.
Read the entire note.
Read sections 19.1-19.5; Chapter 20 is optional, but would be interesting to read if you want to know more about crawling; read the entire Chapter 21.
The main goal is to understand Section 3. You may want to read some other parts especially Sec 1 and Sec 2 to get some background.
Read Section 1, Section 2.1-2.2. The goal is to know how memory-based algorithms work.
Read sections 14.1-14.5
Read sections 16.1-16.4; read the entire Chapter 17.