Volumes VI-IX of HoMe cover the writing of LotR and are kind of a stand-alone part of HoMe (as if anything in Tolkien's legendarium is really stand-alone 😁), so if you want that experience you can buy those volumes without too much concern you're coming into the middle of the story.
You'd also benefit from reading Humphrey Carpenter's biography of Tolkien that gives much of the "real world" background of the writing of LotR.
Just to note that if you have an inkling <ahem> that you might become interested in all of HoMe, you don't have to buy many individual volumes before you've spent more than you would to buy the compiled version. Let me recommend that you check the volumes that you're interested in out of your local public library and get a taste for them before starting to spend money.
This is the only set of the histories of Middle Earth that I could find. Obviously not all of his works, but this is close as you will get for those books for less than $150.
The History of Middle-earth Boxed Set https://www.amazon.com/dp/0358381746/ref=cm_sw_r_apan_glt_fabc_HBZZQFD1NEF2DNXY514K
The problem is in the US. While you may be able to round up a set through used book sources, to get a complete matching set you have to order them from the UK or buy the three-volume omnibus set which by all reports often has printing defects such as the covers being attached upside down or the box being damaged. To get UK sourcing, see this note from a few days ago:
https://old.reddit.com/r/tolkienfans/comments/wenjzy/history_of_middleearth_trade_paperbacks/
There is also a 49% discount on the HMH version (William Morrow) of History of Middle Earth (2020) on Amazon US ("only" 114.85 USD instead of 225.00 USD):
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https://www.amazon.com/History-Middle-earth-Boxed-Set/dp/0358381746/
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I will personally wait for a discount on the HarperCollins one to match my other books, but it might be of interest to some.
https://www.powells.com/book/-9780358381747
https://www.amazon.com/History-Middle-earth-Boxed-Set/dp/0358381746
They're cheaper on Amazon but they're quite heavy and the sleeve is fairly thin so mine got beat up on the way. I looked at it just now and the normal size print is fine to read actually compared to a regular book. It just looks delicate I guess. But it's quite nice overall.
Why not go big? https://www.amazon.com/dp/0358381746/
So this is a wholesaler website that bookstores use. You can’t actually access this page without login information. Here’s a link to the Amazon page though.