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Okay-- first I want to make clear these changes are only to make ANH fit better into the Saga. Personally the first Star Wars movie is the best, the only one that stands on its own, flawlessly and magically. ESB is nice, but it doesn't end and we all know how that turned out ;-P
But to turn this into a Saga that one enjoys best in a 1,2,3,4,5,6 fashion, some sacred stuff will go if I have my way-- because the 1977 movie was the adventure of Luke Skywalker, but then it became "A New Hope" -- Episode IV in the adventures of Anakin Skywalker.
To embrace the Saga, I'd want more context-- I'd want to see what's the Emperor up to? Since this is our first chance to see Darth Vader in action, I'd tweak things to emphasize this point. I'd emphasize things that reveal Anakin inside the suit-- choices that would once make Anakin cringe now fill his life. I'd show some of Alderann to up the stakes of its destruction...
But the biggest change, and the biggest issue heading into the OT, regards the issue that Vader is Luke's Dad. As it stands, Obi Wan chooses to lie to Luke completely and basically set Luke up for a gigantic fall for no good reason. The only way this makes sense is if we can be kept in the dark about Vader's identity-- but now that's impossible. It's not even desirable or necessary-- make the change that redeems Obi Wan and makes him honorable again: have Ben tell Luke that Vader is his father.
It means manipulating the scene where he gives Luke the lightsaber. Have Ben explain that Anakin was a great Jedi and a good man, but that he was seduced by the Dark Side as sometimes happens. Those were harsh times and choices had to be made, so Luke was hidden from his father and Uncle Owen doesn't want Luke to know the truth. But now Princess Leia and the Rebellion need Luke.
Luke's reaction would be to join Ben more quickly, but on his trip to say goodbye to Owen, he finds them dead. His reactions throughout the rest of the movie are already, with minor adjustments, appropriate to acommodate this change.
And man, does it charge the rest of the movie up knowing that Luke already knows Vader's identity. It necessitates tweaks throughout, but not all that much.
Then, in "Empire Strikes Back," the adjustment needs to be made setting up Luke for the big reveal: that Obi Wan is the one who basically killed Anakin. Obi Wan didn't mention this. He lied! Vader doesn't want to kill Luke-- Luke can join him and rule the Galaxy! Defeated, and without options, Luke chooses suicide -- only to be rescued.
Then things carry on-- adjusting for these fixes as they go. (Along with a LOT more when we get to the crap-fest at Jabba's palace and the over-doing it with the Ewoks).
I realize this sounds drastic-- but it sure fixes things for me. Especially as regards fitting ANH into the Saga. In this draft, Obi Wan becomes as honorable as he seemed when the first movie was all there was.